## Questions

Q9.1 Give some illustrations of managerial decision situations in which you think the linear programming technique would be useful.

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.

Q9.3 Do equal distances along a given production process ray in a linear programming problem always represent an identical level of output?

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? Q9.5 Describe the relative distance method used in graphic linear programming analysis. Q9.6 Is the number of isocost, isorevenue, or isoprofit lines in a typical two-input bounded feasible space limited?

Q9.7 In linear programming, why is it so critical that the number of nonzero-valued variables exactly equals the number of constraints at corners of the feasible space? Q9.8 Will maximizing a profit contribution objective function always result in also maximizing total net profits?

Q9.9 The primal problem calls for determining the set of outputs that will maximize profit, subject to input constraints.

A. What is the dual objective function?

B. What interpretation can be given to the dual variables called the shadow prices or implicit values?

C. What does it mean if a dual variable or shadow price equals zero?

Q9.10 How are the solution values for primal and dual linear programming problems actually employed in practice?