Prof. Roh is selling copies of the latest Justin Bieber CD.
There are 3 suppliers (S1,S2,S3) that provide the plastic to make the CDs. Each sup-plier can supply the following amounts at the following prices:
| Supplier | max g available | price/g (in cents) |
| S1 | 2,000 | 3 |
| S2 | 4,000 | 4 |
| S3 | 3,000 | 5 |
Prof. Roh has contracted out 2 plants (P1,P2) that make the CDs. There is a cost to ship each g of plastic from each supplier to the plants (in cents):
| P1 | P2 | |
| S1 | 2 | 3 |
| S2 | 2 | 1 |
| S3 | 1 | 2 |
Each plant has a maximum number of CDs they can produce and di erent costs:
| P1 | P2 | |
| Max CDs can produce | 3,000 | 5,000 |
| Cost (in cents per CD) | 11 | 13 |
Each CD takes 4 g of plastic to make. The CDs are sold for 99 cents each. The CDs are so popular, they are selling o faster than they can make them.
Write a mathematical program to maximize the pro t for Prof. Roh.
You solution should include a clear explaination about your variables, your objective function, your constraints, and indicate whether the program is linear, integer, or non-linear. Feel free to include non-decision variables to make your solution easier to understand.
Note: Do NOT attempt to solve any of the mathematical programs you come up with
