Lecture 6 S11

# Lecture 6 S11 - Lecture 6 Linear programming Source/1...

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Lecture 6 Linear programming Source: /1 / D.R.Anderson, D.J.Sweeney, T.A.Williams. Quantitative Methods for Business, South-Western College Publishing, 11-th edition. Chapter 7. Contents: 6.1 A simple maximization problem 6.2 Graphical solution procedure 6.3 A simple minimization problem Linear programming is a problem-solving approach developed to help managers make decisions. This approach is based on finding an extreme value of some linear function ( objective function ) subject to certain constraints in the form of linear inequalities . We are either trying to maximize or minimize our objective function. That is why these linear programming problems are classified as maximization or minimization problems, or just optimization problems. In this Lecture, we will do problems that involve only two variables, and therefore, can be solved by graphing. We begin by solving a maximization problem. 6.1 A simple maximization problem Example 6.1 RMC, Inc. produces chemical-based products. Three raw materials are used to produce two products: a fuel additive and a solvent base. The three raw materials are blended to form the fuel additive and solvent base as indicated in Table 6.1 . It shows that a ton of fuel additive is a mixture of 0.4 ton of material 1 and 0.6 ton of material 3. A ton of solvent base is a mixture of 0.5 ton of material 1, 0.2 ton of material 2, and 0.3 ton of material 3. Table 6.1 Material requirements per ton for the RMC problem Product Material Fuel Additive Solvent Base Material 1 0.4 0.5 Material 2 0.2 Material 3 0.6 0.3 RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material. Material Amount Available for Production Material 1 20 tons Material 2 5 tons Material 3 21 tons Because of spoilage and the nature of the production process, any materials not used for current production are useless and must be discarded. The accounting department analyzed the production figures, assigned all relevant costs, and arrived at prices for both products that will result in a profit contribution of \$40 for every ton of fuel additive produced and \$30 for every ton of solvent base produced. Problem : determine the number of tons of fuel additive and the number of tons of solvent base to produce in order to maximize total profit .

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We begin with the mathematical statement or mathematical model of this problem. To develop a mathematical model for a linear programming problem we should 1. Describe the Objective. RMC's objective is to maximize the total profit. 2. Describe Each Constraint. Three constraints limit the number of tons of fuel additive and the number of tons of solvent base that can be produced. Constraint
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Lecture 6 S11 - Lecture 6 Linear programming Source/1...

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