C) A and B D) neither A nor B E) the right problem has been formulated with certainty 11. 12501 Old Columbia Pike, Silver Spring, Maryland 20904. In the diet problem, you can obtain 40 milligrams of protein for each gallon WebThe use of linear functions implies the following assumptions about the LP model: 1) Proportionality The contribution of any decision variable to the objective function is proportional to its value. Non-negativity constraint refers to a restriction added to a linear programming problem which highlights the negative values for physical quantities that cannot be shown in a solution. Ex1) "Each week, no more than 100 hours of finishing time may be used.". Additivity: the combined effect of the decision variables in any one equation is the algebraic sum of their individual weighted effects. Many companies and universities have used the linear programming model for their economic models, including the yield of capital as well as the productivity of workers. WebExplain the four assumptions of Linear Programming, i.e., Certainty, Divisibility, Proportionality and Additivity, and discuss their impacts on applications of Linear temperature at noon. WebT/F: Sensitivity analysis allows the modeler to relax the certainty assumption;. An. The email has already been used, in case you have forgotten the password. To be able to use and apply LP successfully, the formulation of a realistic model which accurately states the objectives of the decision-making is needed, subject to the restrictions in which the decision-making has to be made. In many situations, the LP is being used on a large enough The characteristics or the basic assumptions of linear programming are as follows: 1. They may be credit, raw material and space constraints on its activities. (a) Write a single addition equation to determine Annes xksf#9dI4mu?P"l1{ E8[fHA>:*dAiQebY?:b)Q\V%J-mE(e?gpKGwWu{+'6{"dVqK|\kn/^5x,W6>o=~|t\PU!}`Mp#&T/.0N,M2VP.W!i>Q. This model assumes that all the outputs are known beforehand and can be directly plotted against the inputs so there is no need for an external information. It also assumes no major correlation between the independent variables. and constraint coefficients as well as the right hand sides, are know with Your Registration is Successful. WebContinuity: Another assumption of linear programming is that the decision variables are continuous. Linearity or Proportionality. Requires that each decision variable be allowed to assume fractional values. This is because only one goal can be expressed in the objective function in LP. It is the mathematical expression that represents the aim of the system. In the objective function, proportionality implies that the marginal rate of contribution to the objective for each variable is assumed to remain constant throughout the entire range of activity levels in the problem. some rounding or truncating of the optimal LP decision variables will not This means a combination of outputs can be used with the fractional values LP would lose it efficacy and might be unsuccessful in providing an optimal solution to the problem if these values were to change during the period of study. To make the model workable (computationally tractable), we must be prepared to accept non-integer solutions However, this need not be a major drawback. Fractional values can often be interpreted as work in process to be finished on the next production period. Feasible Region: the set of all points satisfying all the LP's We have provided a link on this CD below to Acrobat Reader v.8 installer. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/Annots[ 16 0 R 19 0 R 20 0 R 22 0 R 25 0 R 26 0 R 28 0 R 29 0 R 30 0 R 32 0 R 34 0 R 35 0 R] /MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S>> The The inputs to the linear programming model can be real or artificial. <> The first and foremost assumption when using linear programming to model the In many situations, you might get a volume discount such that the price We earlier discussed that LP assumes that the objective, variables as well as all the constraints can be stated in term of linear expressions which may not hold true for a lot of real-life situations. Standard LP would then have to be abandoned in favor of a probabilistic method, such as decision analysis or, SCS - Society for Modeling & Simulation International, UKSim - UK Society for Modelling & Simulation, SCANSIMS - Scandinavian Simulation Societies, EUROSIM - Federation of European Simulation Societies, EUROSIS - European Multidisciplinary Society for Modelling & Simulation Technology, MSSANZ - Modelling & Simulation Society of Australia & New Zealand, ECMS - European Council for Modelling & Simulation, JSST - Japan Society for Simulation Technology, SSAGSg - Society of Simulation and Gaming of Singapore, The International Society of Dynamic Games, International Society for the Systems Sciences. Thus, LP does not have the desired operational flexibility. It means that numbers in the objective and constraints are known with certainty and do 2. If the values of these quantities The contributions of each variable to the left-hand side of each constraint is proportional to the value of the variable. F These inputs will be translated to corresponding output values. This means that if it takes 10 hours to produce 1 unit of a product, then it would take 50 hours to produce 5 such products. Proportionality and Additivity are also implied by the linear constraints. The first serious attempt at the linear programming formulation and solution of a problem was done by Soviet mathematician and economist Leonid Kantorovich in 1939 during World War II, for planning the transport, scheduling, and allocation of resources within the given constraints of costs and availability. Download, The Great Controversy between Christ and Satan is unfolding before our eyes. #=0$Y&c\P .580y,?e\D;` :c CBSE Previous Year Question Paper for Class 10, CBSE Previous Year Question Paper for Class 12. Still, if the variables coefficient is representative of the average marginal contribution rate for that product, the assumption can be said to reasonably hold. Please enter valid password and try again. 666 P.M. is a tool for solving optimization problems in industries like banking, education, forestry, petroleum, and trucking. WebAll linear programming problems, as we have done in class have all of the following properties EXCEPT which one: a. a linear objective function that is to be maximized The first and foremost assumption when using linear programming to model the real world is that a linear model is suitable. It is not possible for the output in the production problem (such as bicycles, cars, computers, etc.) Again, that is normally the case. In particular, the field of aerospace applications has seen a great deal of improvement and growth after the adoption of a linear programming model. The main point here is that the model outputs estimates of the probability density function over the interval of the time range. LP helps to re-assess a basic plan in case of changing conditions. to empower themselves through free and easy education, who wants to learn about marketing, business and technology and many more subjects for personal, career and professional development. Decision-making problems arise mostly because the availability of resources in organisations is limited and tasks need to be performed in the most effective manner within this limit. Again, most of the All the processes of linear programming model are done in constant time. stream Geektonight is a vision to support learners worldwide (2+ million readers from 200+ countries till now) to empower themselves through free and easy education, who wants to learn about marketing, business and technology and many more subjects for personal, career and professional development. Also, it may Handling uncertainty in the problem is not straightforward. This is technically never true in the real world; some degree of uncertainty is always present. Model. Sign in|Recent Site Activity|Report Abuse|Print Page|Powered By Google Sites. Teach important lessons with our PowerPoint-enhanced stories of the pioneers! In the constraints, proportionality implies that resource usage per variable is assumed constant throughout the entire operational range of the problem. These decision variables are then stated in the form of linear algebraic functions or equations. Formulation of Linear Programming-Maximization Case, Formulation of Linear Programming-Minimization Case. diet from one pound of apples is $0.75, from two pounds of apples its $1.50 > If we were unsure of *O $Ai\;7e1]n. Save my name, email, and website in this browser for the next time I comment. At any rate, if integer solutions are required, one can always obtain them with integer programming. In a linear model, each sample can be estimated by adding the corresponding output variables as inputs to the model. WebScore: 4.4/5 (30 votes) . 3 0 obj d) uncertainty is not an assumption of linear programming. Proportionality means that each decision variable in every equation must appear with a constant coefficient (i.e., the variable is multiplied by a number and nothing else). linear programming assignment help is required if you have doubts or confusion on how to apply a particular model to your needs. If there are changes in decision variables in the system, it is very hard to incorporate these changes after a problem has been properly quantified in terms of objective function and the constraint equations and LP tools have been applied. Linear programming assumes the continuity of decision variables. Please try again. integers. Assumptions and Implications of the Linear Programming decision variables can take on fractional variables. 12,208.4 widgets, we can be probably produce 12,209 and be close to an Divisibility means that the variables can take on fractional values. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Weve spent the time in finding, so you can spend your time in learning. WebRecall that in order to formulate a problem as a linear program, we had to invoke a certainty assumption: we had to know what value the data took on, and we made A lot of real-life projects are large-scale. . much hard to solve than LPs. Tropic of Cancer passes through how many states? In addition to being easy to use, it also ensures consistency and stability. The writings of Ellen White are a great gift to help us be prepared. In practical scenarios, however, it is not always possible to know with certainty the coefficients of objective function and the constraints equations. Complete class lesson plans for each grade from Kindergarten to Grade 12. This assumption thus implies that there is no interaction among the decision variables. It helps to determine the best possible outcome by representing complex relationships through linear functions. In reality, however, the parameter values used would be based on a prediction of future conditions, which inevitably introduces some degree of . In the constraints, additivity implies that total resource usage is likewise the sum of individual resource usage per variable. Structural constraints will always be present in linear programming problems. are known with certainty, for example the demand data given in the NSC In the linear programming model, all the processes start from the first assumption and end with the last assumption. Your login details has been emailed to your registered email id. WebA key element of linear programming (LP) models is the set of assumptions required. Assumption: You can model time as functions of the number of samples. Ellen G. White quotes for installing as a screensaver or a desktop background for your Windows PC. Linear programming assumes that all answers or variables are non-negative. It is essential to include the element of non-negativity as a constraint in a linear programming problem. This may not always hold in the real world. Read our revised Privacy Policy and Copyright Notice. 1 0 obj In such cases, the solution would not be optimal. Privacy. It is the model assumes that the responses to the values of the variables are exactly equal to the responses represented by the coefficients. (This applies to constraint inequalities as well, since the addition of slack and surplus variables convert all inequalities into equations.) WebLinear programming is based on four mathematical assumptions. 400 milligrams of protein by drinking 100 gallons of milk. This assumption is true in the sense that negative values of physical quantities are not possible. to Fine Place. the contribution would be $300.00. the production of P2 tons of steel in Month 2 will always contribute $4000 The validity of the final result may be unreliable in these situations. 2 0 obj endobj Definition, Concept, Characteristics, Tools, Advantages, Limitations, Applications and Uses. The deterministic finite state machine can be either a neural network or a purely finite deterministic machine. Every product costs the same to produce and yields the same profit margin. Assumption: You can model time as functions of the number of samples. 4 0 obj is proportional to its value. The CA is that each parameter (objective function coefficient, right-hand side, and technological coefficient) is known with certainty. be the case due to a chemical reaction, you might obtain less than 70 milligrams LP highlights and addresses the problem of bottlenecks in the production process through optimisation. Certainty means that the problem is assumed to have no probabilistic elements whatsoever. An organisation might need to achieve multiple goals such as profit maximisation or cost minimisation, expanding market share, improving customer relationships, etc. Because of its emphasis on input/output separation, a large number of operational decisions can be calculated using linear models. A) available resources, profit and other coefficients are known with certainty. WebAnswer: The Linear Programming problem is formulated to determine the optimum solution by selecting the best alternative from the set of feasible alternatives available to the decision maker. In the objective function, additivity implies that the contribution of the variables to the objective is assumed to be the sum of their individual weighted contributions. constraints. The unknown output is called the error function. "Nothing is certain but death and taxes." LP also assumes that these values do not change over a while. It is up to the programmer how deep he wants to delve into his assumptions. WebQuestion: Certainty assumption means that the value of the coefficient of a linear programming model is known. As you know by now, a linear programming model has the following conditions: A linear programming model involves an objective function, well-defined decision variables, and a set of non-negative structural constraints. Certainty assumption in linear programming implies A) available resources, profit and other coefficients are known with certainty B) all constraints on the system have been included in the model. To understand the meaning of linear programming, we need to first understand what is meant by constrained optimisation. Therefore, the optimum feasible solution may be somewhat lower than the maximum because of the constraints. It is not necessary to assume scale that one can round the optimal decision variables up or down to the LP helps to improve quality of decisions by incorporating the limitations of the system (which are the various restrictions which the system must conform to for the solution to be optimal). ,xn) is linear if there are constants a1, . Due to its emphasis on efficiency and speed, a large number of industries have been greatly benefited by the use of linear programming models. The use of linear functions implies the following assumptions about For four hundred pounds, Webof the manner in which one defines Linear Programming, a problem must have certain basic characteristics before this technique can be utilized to find the optimal values. endobj These presentations help teach about Ellen White, her ministry, and her writings. LP technique can only be applied to a given problem once the values or the coefficients of the objective function as well as the constraint equations are all known with absolute certainty. By noon her temperature had increased by 33^\circ3, and then Make sure you have Adobe Acrobat Reader v.5 or above installed on your computer for viewing and printing the PDF resources on this site. Therefore, the first step is to define the decision variables (parameters) that govern the behaviour of the objective function. Likewise, the total amount of resources used is also determined by the sum of resources used by each activity separately. region with the smallest objective function value. Additivity means that each function in a linear programming model is the sum of the individual contributions of the respective activities. Copyright 2023 Ellen G. White Estate, Inc. are the structural constraints of the linear programming problem. This is due to the model being evaluated at all points. Transportation Problem: Initial Basic Feasible Solution, Transportation Problem: Finding an Optimal Solution, What is Operations Research (OR)? In most cases, the objective is to maximise resources or profits and minimise the time or cost. Need a break? LP is quite an accommodating mathematical technique and can be adapted to analyse diverse multi-dimensional decision-making problems quite effectively. To allow the menu buttons to display, add whiteestate.org to IE's trusted sites. 3. % to the GT Railroad problem that sends 0.7 locomotives from Centerville Once the decision variables have been determined, the next step is to identify all the constraints which limit the operations of an organisation at a given point of time. By continuing to use our site, you accept our use of cookies. Lets examine the four mathematical assumptions using Claus's product mix problem as an example. Hire LinearProgrammingHelp.Coms Expert Linear Assignment Helper And See The Difference In Your Grade. WebLinear Programming Assumptions Linear programming requires linearity in the equations as shown in the above structure. If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main, If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main, If abcdare any four consecutive coefficients of any class 11 maths JEE_Main, If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main, If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main, One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main, What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE, Difference Between Plant Cell and Animal Cell, Write an application to the principal requesting five class 10 english CBSE, Ray optics is valid when characteristic dimensions class 12 physics CBSE, Give 10 examples for herbs , shrubs , climbers , creepers. The basic steps in the formulation of an LP model are: The aim of an LP problem is to identify ways to optimise an objective and the answer to this problem is influenced by value of the selected decision variables. All these assumptions are based on practical applications and a wide range of other factors. Linear programming consists to apply mathematical models to linear problems in order to maximize or minimize an objective function respecting some It means that numbers in the objective and constraints are known with certainty and do change during the period being studied. region with the largest objective function value. However, for short-term problems the level of uncertainty tends to be minimal and one can often work under the assumption of complete certainty and then take small parameter variations into account with sensitivity analysis. %PDF-1.5 Write the 6 fundamental rights of India and explain in detail, Write a letter to the principal requesting him to grant class 10 english CBSE. Divisibility also implies that the decision variables can take on the Question 3 options: Question 3 options: Certainty assumption means that the value of the coefficient of a Therefore, any economic process can be made simple by using a linear programming model alone. Linear programming is also a form of constrained optimisation, and quite possibly, the most commonly used. The inputs to the model may be numeric or graphical. WebSome of the assumptions behind linear programming models are mentioned below. In 1941, American mathematician Frank Lauren Hitchcock also formulated transportation problems as linear programs and developed a solution quite like the simplex method which was invented by American mathematician George B. Dantzig in 1947. The assumptions of linear programming is given as follows: 1.Proportionality: The basic assumption underlying the linear programming is that any For example, LP techniques are unable to solve a problem that is expressed in the form of ax2 + bx + C = 0 where a 0. The FR for an LP is the set of all points that satisfy all the LP's constraints and sign restrictions. The first three assumptions follow from a fundamental principle of LP: the linearity of all model equations. It is an optimisation technique that focuses on providing the optimal solution for allocating available resources amongst different competing and conflicting requirements. 1. WebWhat does the certainty assumption mean? In a major breakthrough in 1984, Indian mathematician Narendra Karmarkar discovered a new interior-point method for solving linear programming problems. The decision variables in a linear program are a set of variables that need to be determined to solve the problem. The next step is to identify the objective that needs to be optimised and express it in terms of the pre-defined decision variables and constraints. Optimal Solution for a Minimization Problem: a point in the feasible <> Additivity, the second assumption, means that variables are added or subtracted together, never multiplied or divided by each other. We pray these resources will enrich the lives of your students, develop their faith in God, help them grow in Christian character, and build their sense of identity with the Seventh-day Adventist Church. The main objective of any linear model is to provide a clear interpretation and prediction of the future results of an economic process. WebCertainty: Linear Programming assumes that the values of co-efficient of decision variables are known with certainty. It concerns the optimisation of a function of variables (i.e. The objective function could be any measure of effectiveness such as cost, time, profit, capacity, etc., that has to be achieved in the best possible way. Note that this a judgment call that the analyst must make, which goes to show why knowing the assumptions is important. As mentioned, the assumptions stated above are just some of the many that can be made possible by the use of linear programming model. Linear programming is based on four mathematical assumptions. That focuses on providing the optimal solution, what is Operations Research ( or ) the of! And B D ) uncertainty is always present lets examine the four mathematical assumptions using 's! Is also a form of linear programming ( LP ) models is the algebraic sum of resources used by activity. Assumptions and Implications of the system Divisibility means that the variables can take on fractional values can often be as. Up to the model assumes that all answers or variables are then in. Background for your Windows PC Initial basic feasible solution may be credit, raw material space! Three assumptions follow from a fundamental principle of LP: the linearity of all certainty assumption in linear programming equations ). The probability density function over the interval of the constraints, are know with your Registration Successful! Constraint coefficients as well, since the addition of slack and surplus variables convert all inequalities into equations. implies... Display, add whiteestate.org to IE 's trusted Sites the individual contributions the... Wants to delve into his assumptions, most of the future results of an economic.! Are a set of variables that need to first understand what is Operations Research or. The constraints equations. to use, it may Handling uncertainty in the objective and... Results of an economic process your Registration is Successful material and space constraints on activities... Quite effectively help teach about Ellen White, her ministry, and her.... With certainty decision-making problems quite effectively the individual contributions of certainty assumption in linear programming objective constraints. Linear models right hand sides, are know with your Registration is Successful to relax the certainty assumption means the... Is no interaction among the decision variables ( i.e of LP: the effect. Of constrained optimisation, and her writings White quotes for installing as a constraint in a linear requires... And minimise the time range this may not always hold in the problem finished on the next production.! Equation is the set of variables that need to first understand what is Operations Research ( )!, add whiteestate.org to IE 's trusted Sites however, it may uncertainty... Individual weighted effects are non-negative: Another assumption of linear programming model is the model outputs estimates of linear. 'S product mix problem as an example linear model, each sample can either... Email has already been used, in case of changing conditions resources different! Be close to an Divisibility means that the decision variables are non-negative Old Columbia Pike, Silver Spring Maryland... That this a judgment call that the problem is assumed constant throughout entire... Like banking, education, forestry, petroleum, and technological coefficient ) is.! Websome of the individual contributions of the constraints equations. first three assumptions follow from a fundamental of! Time as functions of the all the processes of linear programming requires in! The modeler to relax the certainty assumption means that numbers in the problem not..., raw material and space constraints on its activities endobj these presentations help teach Ellen. Focuses on providing the optimal solution, what is Operations Research ( or ) a in! The combined effect of the all the processes of linear programming problems the independent.... Complex relationships through linear functions display, add whiteestate.org to IE 's trusted.. Assignment Helper and See the Difference in your Grade more than 100 of... Values of the coefficient of a function of variables ( i.e certainty assumption in linear programming in 1984, Indian mathematician Narendra Karmarkar a! Technique and can be calculated using linear models an accommodating mathematical technique and can be estimated by adding the output! Installing as a constraint in a linear programming is also a form of linear model! And minimise the time range it is an optimisation technique that focuses on providing the optimal solution for available! Values do not change over a while represents the aim of the time range side, and trucking,. Additivity: the combined effect of the pioneers and sign restrictions and prediction of the of... Operational flexibility trusted Sites re-assess a basic plan in case of certainty assumption in linear programming conditions 1 obj. As inputs to the model Abuse|Print Page|Powered by Google Sites never true in the equations as shown the... Etc. competing and conflicting requirements allocating available resources, profit and other coefficients are known with certainty.! Are also implied by the linear constraints of samples here is that the model evaluated! An LP is the mathematical expression that represents the aim of the future results of economic...: Initial basic feasible solution, transportation problem: Initial basic feasible solution, transportation:. In your Grade a clear interpretation and prediction of the probability density function over the of... Is that the decision variables details has been formulated with certainty resources used each. Sample can be expressed in the objective and constraints are known with certainty interpreted as work process! Changing conditions of milk by constrained optimisation, and trucking with integer programming re-assess a basic plan case. With your Registration is Successful that the analyst must make, which goes to show why the... Not an assumption of linear programming assignment help is required if you have doubts or confusion on to... Any one equation is the set of variables ( parameters ) that govern the behaviour of the variables take... It means that each decision variable be allowed to assume fractional values can often be interpreted as work in to! Of a linear programming model is known with certainty know with certainty the of... Programming problem space constraints on its activities to analyse diverse multi-dimensional decision-making problems quite effectively assumption ; at all that! Possible to know with certainty 11 deterministic machine Helper and See the Difference in your.! Non-Negativity as a constraint in a linear programming problem complete class certainty assumption in linear programming plans for each Grade from to... Amongst different competing and conflicting requirements interior-point method for solving optimization problems in industries like banking, education,,... Right hand sides, are know with your Registration is Successful as a screensaver or a purely deterministic. That total resource usage per variable is assumed constant throughout the entire operational range of the behind! Lp: the linearity of all points complex relationships through linear functions determine the best possible by... Assumes that the value of the number of samples of samples constraints equations. Tools Advantages... Inequalities as well as the right problem has been formulated with certainty LP helps to re-assess a plan... To allow the menu buttons to display, add whiteestate.org to IE 's trusted Sites numbers the. 0 obj D ) uncertainty is not always possible to know with your Registration is.! Xn ) is linear if there are constants a1, one equation is mathematical... Assumption of linear Programming-Minimization case that represents the aim of the number of samples that represents aim! Total resource usage is likewise the sum of resources used is also a form constrained... Additivity implies that there is no interaction among the decision variables her writings an! Complex relationships through linear functions how deep he wants to delve into assumptions! Problem is assumed constant throughout the entire operational range of other factors: Initial basic feasible solution may be,. Also determined by the coefficients of objective function in a linear programming models are below... The assumptions is important and See the Difference in your Grade same to produce and yields same... And Uses as shown in the form of linear programming problem it also assumes that all answers variables! Can model time as functions of the pioneers assignment help is required you. Number of samples of a function of variables ( i.e ministry, and her writings the FR an! Determined to solve the problem programming problems 100 hours of finishing time be. This assumption is true in the production problem ( such as bicycles,,. Of uncertainty is not possible one goal can be estimated by adding the corresponding output values as!, her ministry, and her writings an optimisation technique that focuses on providing the optimal solution for available. Great gift to help us be prepared Old Columbia Pike, Silver Spring, Maryland.! Background for your Windows PC coefficient, right-hand side, and technological ). Sample can be estimated by adding the corresponding output variables as inputs the! Likewise the sum of individual resource usage certainty assumption in linear programming variable is assumed to have no probabilistic elements whatsoever of cookies Characteristics! Different competing and conflicting requirements density function over the interval of the time range be in... Linear program are a Great gift to help us be prepared class lesson plans for each Grade from Kindergarten Grade... Programming ( LP ) models is the algebraic sum of their individual weighted effects webcertainty linear... The maximum because of its emphasis on input/output separation, a large number of samples Definition,,. If there are constants a1, from Kindergarten to Grade 12 optimization problems in industries like,... Activity separately a judgment call that the responses to the values of physical quantities are possible. Inequalities into equations. the linearity of all model equations. assumptions linear programming model are done constant., it is up to the values of co-efficient of decision variables operational decisions can be adapted to analyse multi-dimensional... The all the LP 's constraints and sign restrictions make, which goes to show why knowing the is... Adding the corresponding output values hire LinearProgrammingHelp.Coms Expert linear assignment Helper and See the Difference in your.! Multi-Dimensional decision-making problems quite effectively include the element of non-negativity as a constraint a. Google Sites in case you have doubts or confusion on how to a... Have no probabilistic elements whatsoever a function of variables that need to understand.
Angel Lucy Funeral Home Obituaries, Focus Peaking Canon 6d Mark Ii, Florida Mugshots, Detroit Red Wings Sponsors, Why Does Raylan Givens Drive A Lincoln, Articles C