The Jones, Jones, Smith, and Rodman commodities trading firm knows the prices at which it will be able to buy and sell a certain commodity during the next 4 months. The buying price ( ci) and selling price ( pi) for each of the given months ( i) are as follows:
|
Monthi
|
|
|
1
|
2
|
|
3
|
4
|
|
ci
|
$5
|
$6
|
|
$7
|
$8
|
|
pi
|
4
|
8
|
|
6
|
7
|
The firm's warehouse has a maximum capacity of 10,000 bushels. At the beginning of the first month, 2,000 bushels are in the warehouse. The trading firm wants to know the amounts that should be bought and sold each month in order to maximize profit. Assume that no storage costs are incurred and that sales are made at the beginning of the month, followed by purchases.
- Formulate a linear programming model for this problem.
- Solve the model by using the computer.