7. Minty has \(\pounds 250000\) to allocate to three investment schemes. She will allocate the money to these schemes in units of \(\pounds 50000\). The net income generated by each scheme, in \(\pounds 1000\) s, is given in the table below.
| \(\mathbf { \pounds 0 }\) | \(\mathbf { \pounds 5 0 0 0 0 }\) | \(\mathbf { \pounds 1 0 0 0 0 0 }\) | \(\mathbf { \pounds 1 5 0 0 0 0 }\) | \(\mathbf { \pounds 2 0 0 0 0 0 }\) | \(\mathbf { \pounds 2 5 0 0 0 0 }\) |
| Scheme1 | 0 | 60 | 120 | 180 | 240 | 300 |
| Scheme 2 | 0 | 65 | 125 | 190 | 235 | 280 |
| Scheme 3 | 0 | 55 | 110 | 170 | 230 | 300 |
Minty wishes to maximise the net income. She decides to use dynamic programming to determine the optimal allocation, and starts the table shown in your answer book.
- Complete the table in the answer book to determine the amount Minty should allocate to each scheme in order to maximise the income. State the maximum income and the amount that should be allocated to each scheme.
- For this problem give the meaning of the table headings
- Stage,
- State,
- Action.