A fruit farmer supplies raspberries and blueberries to a leading supermarket. She is contracted to supply at least 100 kg of raspberries and 50 kg blueberries each week. The supermarket requires that the total weight of fruit delivered must be at least 200 kg. In a typical week she can harvest a maximum of 200 kg of raspberries and 300 kg of blueberries.
The cost of supplying a kilo of raspberries is $4.40, and the corresponding figure for blueberries is $3.10.

(a) Formulate this as a linear programming problem if the farmer’s strategy is to minimise total cost.

(b) Sketch the feasible region.

(c) Write down the coordinates of the corners of the feasible region.

(d) How many kilos of raspberries and blueberries should the farmer supply each week to the supermarket?

(e) The selling prices of a kilo of raspberries and a kilo of blueberries are $8 and $10, respectively. Work out the maximum weekly profit that the supermarket could make.