Brick orders: distinguish a fixed-profit system from cost minimisation

A brick manufacturer has a depot with a stock of 30 000 bricks. He receives orders from three builders P, Q and R for a total of 30 000 bricks and the total order from builders P and R is twice that of builder Q.

(a) If the profit earned from each brick is $3 and the manufacturer earns $9 600 more in profit from builder R compared to builder P, find the number of orders from each builder.4 marks

(b) Instead of using the information in part (a), it is now given that the cost of transporting each brick to builders P, Q and R from the depot is $0.04, $0.02 and $0.03 respectively. If there is a minimum order of 1000 bricks from each builder, what are the orders that the manufacturer should accept so as to keep the cost of transportation a minimum?3 marks