You own a wheat warehouse with a capacity of 20,000 bushels. At the beginning of month 1 you have 6000 bushels of wheat. Each month, wheat can be bought and sold at the price per bushel shown in the table below:
| Month |
Selling Price $ |
Purchase Price $ |
| 1 |
3 |
8 |
| 2 |
6 |
8 |
| 3 |
7 |
2 |
| 4 |
1 |
3 |
| 5 |
4 |
4 |
| 6 |
5 |
3 |
| 7 |
5 |
3 |
| 8 |
1 |
2 |
| 9 |
3 |
5 |
| 10 |
2 |
5 |
At the beginning of each month you observe the amount of wheat you have on hand. You first sell some quantity ranging from zero to the entire amount that you have. You then buy as much wheat as you wish subject to the constraint that the amount you buy plus the unsold portion of the month's beginning inventory cannot exceed the warehouse capacity.
Formulate and solve an LP to find the amounts bought and sold each month so that the net revenue at the end of 10 months is maximized.