Hello s3a

The maximum profit will occur at one of the vertices of the shaded polygon. You could begin by sketching on the graph a profit line, choosing a suitable value of P; e.g. P = 60 giving x + 3y = 60. Then any other profit line will be parallel to this one, and so you then move the line up the graph until it is at its highest point while still retaining at least one point within the shaded area.

However, in this example, the easiest way to find out which vertex is best is probably by trial and error, since the arithmetic is simple. The only realistic possibilities are (60, 40) and (100, 0). So:

- At (60, 40) he sells 60 bags of coffee and 40 boxes of chocolate. How much profit should he make? How much did he actually make?
- Repeat for (100, 0).
- Choose the best one. Don't forget to answer the question: write down the decrease in his earnings.

Grandad