1. A group of young entrepreneurs earns a (temporarily) steady living by acquiring inadequately supervised items from electronics stores and re-selling them. Each item has a street value, a weight, and a volume; there are limits on the numbers of available items, and on the total weight and volume that can be managed at one time. Suppose that the weight and volume limits are 500 pounds and 300 cubic feet, and the available items are described below:
Value Weight Volume Available
TV 50 35 8 20
cell phone 15 5 1 50
IPad 85 4 2 20
MP3 player 40 3 1 30
DVD player 50 15 5 30
Camcorder 120 20 4 15
(a) Formulate this problem as a linear program.
(b) Solve the problem.
2. A small manufacturing operation produces six kinds of parts, using three machines. For the coming month, a certain number of each part is needed, and a certain number of parts can be accommodated on each machine; to complicate matters, it does not cost the same amount to make the same part on di_erent machines. Speci_cally, the costs and related values are as follows:
Part
Machine 1 2 3 4 5 6 Capacity
1 3 3 2 5 2 1 80
2 4 1 1 2 2 1 30
3 2 2 5 1 1 2 160
Required 10 40 60 20 20 30
(a) Formulate the problem as a linear program Hint: compare this problem with transporta- tion model
(b) Solve the problem.
(c) Suppose that there exists an option of increasing capacity by upgrading any of the machines. Which machine you would suggest should be upgraded and why? Describe the analytical procedure that you used in order to arrive to your conclusion.