Chap 3 WE - Worked Examples for Chapter 3 Example for...

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Worked Examples for Chapter 3 Example for Section 3.1 The Apex Television Company has to decide on the number of 27- and 20-inch sets to be produced at one of its factories. Market research indicates that at most 40 of the 27-inch sets and 10 of the 20-inch sets can be sold per month. The maximum number of work- hours available is 500 per month. A 27-inch set requires 20 work-hours and a 20-inch set requires 10 work-hours. Each 27-inch set sold produces a profit of $120 and each 20-inch set produces a profit of $80. A wholesaler has agreed to purchase all the television sets produced if the numbers do not exceed the maxima indicated by the market research. (a) Formulate a linear programming model for this problem. The decisions that need to be made are the number of 27-inch and 20-inch TV sets to be produced per month by the Apex Television Company. Therefore, the decision variables for the model are x 1 = number of 27-inch TV sets to be produced per month, x 2 = number of 20-inch TV sets to be produced per month. Also let Z = total profit per month. The model now can be formulated in terms of these variables as follows. The total profit per month is Z = 120 x 1 + 80 x 2 . The resource constraints are: (1) Number of 27-inch sets sold per month: x 1 40 (2) Number of 20-inch sets sold per month: x 2 10 (3) Work-hours availability: 20 x 1 + 10 x 2 500. Nonnegativity constraints on TV sets produced: x 1 0 x 2 0 With the objective of maximizing the total profit per month, the LP model for this problem is
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Maximize Z = 120 x 1 + 80 x 2 , subject to x 1 40 x 2 10 20 x 1 + 10 x 2 500 and x 1 0, x 2 0. (b) Use the graphical method to solve this model. The constraint,
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Chap 3 WE - Worked Examples for Chapter 3 Example for...

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