5 [Figure 3, printed on the insert, is provided for use in this question.]
A small firm produces high quality cabinets.
It can produce up to 4 cabinets each month.
Whenever at least one cabinet is made during that month, the overhead costs for that month are \(\pounds 300\).
It is possible to hold in stock a maximum of 2 cabinets during any month.
The cost of storage is \(\pounds 50\) per cabinet per month.
The orders for cabinets are shown in the table below. There is no stock at the beginning of January and the firm plans to clear all stock after completing the April orders.
| Month | January | February | March | April |
| Number of cabinets required | 3 | 3 | 5 | 2 |
- Determine the total cost of storing 2 cabinets and producing 3 cabinets in a given month.
- By completing the table of values on Figure 3, or otherwise, use dynamic programming, working backwards from April, to find the production schedule which minimises total costs.
- Each cabinet is sold for \(\pounds 2000\) but there is an additional cost of \(\pounds 300\) for materials to make each cabinet and \(\pounds 2000\) per month in wages. Determine the total profit for the four-month period.