- A company wishes to plan its production of a particular item over the coming four months based on its current orders. In each month the company can manufacture up to three of the item with the costs according to how many it makes being as follows:
| No. of Items Produced | 0 | 1 | 2 | 3 |
| Cost in Pounds | 0 | 5500 | 9700 | 13100 |
There are no items in stock at the start of the period and the company wishes to meet all its orders on time and have no stock left at the end of the 4-month period. If any items are not to be supplied in the month they are made there is also a storage cost incurred of \(\pounds 400\) per item per month.
The orders for each of the four months being considered are as follows:
| Month | March | April | May | June |
| No. of Orders | 1 | 2 | 4 | 1 |
Use dynamic programming to find how many of the item the company should make in each of these four months in order to minimise the total cost for this period.
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