8. A factory can process up to five units of carrots each month.
Each unit can be sold fresh or frozen or canned.
The profits, in \(\pounds 100\) s, for the number of units sold, are shown in the table.
The total monthly profit is to be maximised.
| Number of units | 0 | 1 | 2 | 3 | 4 | 5 |
| Fresh | 0 | 45 | 85 | 120 | 150 | 175 |
| Frozen | 0 | 45 | 70 | 100 | 120 | 130 |
| Canned | 0 | 35 | 75 | 125 | 155 | 195 |
Use dynamic programming to determine how many of the five units should be sold fresh, frozen and canned in order to maximise the monthly profit. State the maximum monthly profit.
(Total 12 marks)