Answer only letter E from exercise #36. Letter E is on the second page

Part 1 Linear Programming b. What is the maximum price the store would be justified in paying for additional pine bark? c. What is the marginal value of labor? Over what range is this value in effect? d. The manager obtained additional machine time through better schedul- ing. How much additional machine time can be effectively used for this operation? Why? e. If the manager can obtain either additional pine bark or additional stor- age space, which one should be chosen and how much should be obtained (assuming additional quantities cost the same as usual)? f. If a change in the chip operation would increase the profit on chips from $6 per bag to $7 per bag, would the optimal quantities change? Would the value of the objective function change? If so, what would the new value(s) be? 36. A firm produces jars of chilled fruit that are sold to restaurants. Three va- rieties of fruit are sold: California mix (x), Florida mix (x2), and Hawaiian mix (x3). A linear programming model for the process is: maximize 4x, + 3x2 + 6xz (profit) subject to Oranges 32, + 2x2 + 1x, 5 920 pounds Grapefruit 2x + 2x2 + 2x3 s 900 pounds Pineapple 1x, + 2.x2 + 3x3 s 930 pounds Peeling/cutting 1.2x, + 1.4x2 + 1.5x2 = 1,260 minutes Mixing/packaging 1x + 2x2 + 1x: $ 600 minutes X1, 42, x3 = 0 The equipment used for peeling and cutting must be replaced. The new Chapter 6 Postoptimality Analysis 249 this change have on the optimal values of the basis variables and on profit? What would the unit profit on the Florida mix have to be before it would become profitable to produce? If management had a choice of obtaining more oranges or more pineap- ples, which one should be chosen? Why? >@ Management has just learned that an additional 50 pounds of pineapple are on hand. What will the optimal values in the Quantity column change to? > Management is considering making changes that will cause the profit on the Hawaiian mix to be $8 per unit. Would this affect the solution? Will it affect the optimal value of the objective function? A Management is considering a change in equipment that would result in increasing the profit on the Hawaiian mix to $8 per unit, but result in decreasing the profit on the California mix by $1. Would these changes be within the range of sensitivity? If so, how much would the optimal profit change? 37. Use a computer package to perform sensitivity analysis on the LP model given in Problem 33, and then use that information to answer the questions listed in Problem 33. 38. Use a computer package to perform sensitivity analysis on the LP model given in Problem 34, and then use those results to answer parts (a)-(c) of Problem 34. 39. Use a computer package to perform sensitivity analysis on the LP model given in Problem 35, and then use the results to answer the questions for that problem 40. /Use a computer package to perform sensitivity analysis on the LP model given in Problem 36, and then use the results to answer the questions (ex- cept d) for that problem. 41. Special D, Inc., is a new firm that is engaged in recycling. Its main facility uses a three-step system to process beverage containers. A consultant has developed the following LP model of the process: maximize 14Q + 11R + 157 (revenue) subject to Sorting 2.4Q + 3.0R + 4.07 3 960 minutes Crushing 2.5Q + 1.8R + 2.41 s 607 minutes Packing 12Q + 18R + 241 = 3,600 minutes Q, R, and T 20 7