Problem 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
|
a
|
35
|
8
|
20
|
|
cell phone
|
15
|
5
|
1
|
50
|
|
IPad
|
85
|
b
|
2
|
20
|
|
MP3 player
|
40
|
3
|
1
|
30
|
|
DVD player
|
c
|
15
|
5
|
30
|
|
camcorder
|
120
|
20
|
4
|
15
|
Use the following directions to obtain values for parameters: a is the last two digits of your AU id, b is the last digit of your birthday, and c is the last two digits of your phone number. For example, I would have a = 19, since my AU id is azv0019, b = 8, since my birthday is on 28th and c = 25, for phone number 334-844-1425.
(a) Formulate this problem as a linear program.
(b) Solve the problem. What should be the items acquired and what is the total value?
(c) Solve the problem using NEOS. Submit the email document that you received from NEOS to Canvas.
(d) If your optimal solution does not prescribe taking and cell phones: what should its value be in order to make it worth taking? Otherwise, what should its value be in order to make it not worth taking?
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 different machines. Specifically, the costs and related values are as follows:
|
Machine
|
Part
|
Capacity
|
|
1
|
2
|
3
|
4
|
5
|
6
|
|
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 to transportation model discussed in class.
(b) Solve the problem.
(c) Suppose that there exists an option of increasing capacity by upgrading any of the machines. Which machine would you suggest should be upgraded and why? Describe how you arrive to your conclusion.