The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 board feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 board feet of redwood; each picnic table takes 6 labor hours and 35 board feet of redwood. Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit? Use the graphical LP approach.

7-19.
MSA Computer Corporation manufactures two models of smartphones, the Alpha 4 and the Beta 5. The firm employs five technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next month’s operations. It requires 20 labor hours to assemble each Alpha 4 computer and 25 labor hours to assemble each Beta 5 model. MSA wants to see at least 10 Alpha 4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each. Determine the most profitable number of each model of smartphone to produce during the coming month.

7-31
Consider the following LP problem: Maximize profit = 5X + 6 Y subject to 2X + Y … 120 2X + 3Y … 240 X, Y Ú 0 (a) What is the optimal solution to this problem? Solve it graphically. (b) If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution? (c) Instead of an increase in the profit coefficient X to $8, suppose that profit was overestimated and should only have been $3. Does this change the optimal solution?

9-13
Finnish Furniture manufactures tables in facilities located in three cities—Reno, Denver, and Pitts-burgh. The tables are then shipped to three retail stores located in Phoenix, Cleveland, and Chicago. Management wishes to develop a distribution schedule that will meet the stores’ demands at the lowest possible cost. The shipping cost per unit from each of the sources to each of the destinations is shown in the following table:

TO FROM RENO DENVER PITTSBURGH PHOENIX CLEVELAND CHICAGO 16 14 12 10 12 18 19 13 12 The available supplies are 120 units from Reno, 200 from Denver, and 160 from Pittsburgh. Phoenix has a demand of 140 units, Cleveland has a demand of 160 units, and Chicago has a demand of 180 units. How many units should be shipped from each manufacturing facility to each of the retail stores if cost is to be minimized? What is the total cost?