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4-13 Consider the Win Big Gambling Club media selec- tion example discussed in section 3.3 (page 73) of Chapter 3. Use the Sensitivity Report for this LP model (shown in Screenshot 4-6) to answer the fol- lowing questions. Each question is independent of the others. What is the impact on the audience coverage under the following scenarios? (a) Management approves spending $200 more on radio advertising each week. (b) The contractual agreement to place at least five radio spots per week is eliminated. (c) The audience reached per ad increases to 3,100. (d) There is some uncertainty in the audience reached per TV spot. For what range of values for this OFC will the current solution remain optimal?

4-28 The Classic Furniture Company is trying to deter- mine the optimal quantities to make of six possible products: tables and chairs made of oak, cherry, and pine. The products are to be made using the follow- ing resources: labor hours and three types of wood. Minimum production requirements are as follows: at least 3 each of oak and cherry tables, at least 10 each of oak and cherry chairs, and at least 5 pine pine chairs.

The Excel layout and LP Sensitivity Report for Classic Furnitures problem are shown in Screen- shots 4-13A and 4-13B, respectively. The objective function coefficients in the Screenshots refer to unit profit per item. Each of the following questions is independent of the others. (a) What is the profit represented by the objective function, and what is the production plan? (b) Which constraints are binding? (c) What is the range over which the unit profit for oak chairs can change without changing the production plan? (d) What is the range over which the amount of available oak could range without changing the combination of binding constraints? (e) Does this Sensitivity Report indicate the pres- ence of multiple optima? How do you know? (f) After production is over, how many pounds of cherry wood will be left over? (g) According to this report, how many more chairs were made than were required?

4-29 Consider the Classic Furniture product mix problem (Problem 4-28). For each of the following situations, what would be the impact on the production plan and profit? If it is possible to compute the new profit or production plan, do so. (a) The unit profit for oak tables increases to $83. (b) The unit profit for pine chairs decreases to $13. (c) The unit profit for pine tables increases by $20. (d) The unit profit for cherry tables decreases to $85. (e) The company is required to make at least 20 pine chairs. (f) The company is required to make no more than 55 cherry chairs.

4-30 Consider the Classic Furniture product mix problem (Problem 4-28). For each of the following situations, what would be the impact on the production plan and profit? If it is possible to compute the new profit or production plan, do so. (a) The number of labor hours expands to 1,320. (b) The amount of cherry wood increases to 3,900. (c) The number of labor hours decreases to 950. (d) The company does not have a minimum require- ment for cherry chairs.