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Unformatted text preview: Chapter 9 Linear Programming QUESTIONS AND ANSWERS Q9.1 Give some illustrations of managerial decision situations in which you think the linear programming technique would be useful. Q9.1 ANSWER Linear programming can be used for solving any type of constrained optimization problem where the relations involved can be approximated by linear equations. Linear revenue, cost, and profit relations will be observed when output prices, input prices, and average variable costs are constant. Linear programming is particularly relevant when slack or excess capacity is possible. Although feasible, linear programming techniques are typically not employed in problems where the constraints can all be treated as equalities, because alternate and somewhat simpler solution techniques are available for such problems. Linear programming has been used to determine optimal production schedules, investment portfolios, delivery routes, input combinations, product mixes, advertising media mixes, capital budgets, and so on. Q9.2 Why can't linear programming be used in each of the following circumstances A. Strong economies of scale exist. B. As the firm expands output, the prices of variable factors of production increase. C. As output increases, product prices decline. Q9.2 ANSWER In all three cases, parts A through C, the condition identified implies a violation of the linearity assumption necessary for the use of linear programming techniques. Q9.3 Do equal distances along a given production process ray in a linear programming problem always represent an identical level of output? Q9.3 ANSWER Yes, equal distances along a given production process ray always represent an identical level of output. This stems from the fact that constant returns to scale must be operative in any linear programming problem. 218 Chapter 9 Q9.4 Assume that output can be produced only using processes A and B. Process A requires inputs L and K to be combined in the fixed ratio 2L:4K, and process B requires 4L:2K. Is it possible to produce output efficiently using 3L and 3K? Why or why not? Q9.4 ANSWER If Process A requires 2L:4K and process B requires 4L:2K, then it is possible to efficiently produce output using a 3L and 3K combination by using each process to produce onehalf of total output. Even with a limited number of available production methods, it is possible to produce output with a wide variety of input combinations by using a combination of production processes. Graphically, this is illustrated in Figure 9.2. Q9.5 Describe the relative distance method used in graphic linear programming analysis. Q9.5 ANSWER For feasible production points located between two production processes, both processes will be used in production, and these points will be located on isoquants....
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 Summer '10
 LEITER
 Linear Programming, Optimization, linear programming problem, high fiber

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