Question : WAREHOUSE PROBLEM
A large peanut warehouse has the capacity for indefinitely storing 200 tons of peanuts. There are currently 80 tons of peanuts in the warehouse and the forecasting department has come up with what it thinks are going to be the per-ton prices for peanuts at the next five monthly peanut sales.
These projected prices are listed. There is also a storage cost of S5 per ton assessed on peanuts left in the warehouse after each sale.
Because the price of peanuts fluctuate, it is possible to make a profit by buying low and selling high For example, the warehouse could buy peanuts in month 2 at $100 per ton, store them until month 4, and then sell them at $180 per ton.
The question is:
What should the buying and selling program be in order to maximize the total profit made at the next five peanut sales?
This problem is different in structure from the previous ones in a very important way; namely, it is dynamic in the sense that what we do in one period affects what we can do in later periods.
|
Month
|
Price
|
|
1
|
$120
|
|
2
|
$100
|
|
3
|
$150
|
|
4
|
$180
|
|
5
|
$130
|