Question: A firm produces two commodities A and B. The firm has three factories that jointly produce both commodities in the amounts per hour given in the following table:
The firm receives an order for 300 units of A and 500 units of B. The costs per hour of running factories 1, 2, and 3 are respectively 10 000, 8000, and 11 000.
(a) Let y1, y2, and y3, respectively, denote the number of hours for which the three factories are used. Write down the linear programming problem of minimizing the costs of fulfilling the order.
(b) Write down the dual and solve it. Then find the solution of the problem in part (a).
(c) By how much will the minimum cost of production increase if the cost per hour in factory 1 increases by 100?