(a) A firm produces two different kinds A and B of a commodity. The daily cost of producing x units of A and y units of B is
C(x, y) = 2x2 - 4xy + 4y2 - 40x - 20y + 514
Suppose that the firm sells all its output at a price per unit of $24 for A and $12 for B. Find the daily production levels x and y that maximize profit.
(b) The firm is required to produce exactly 54 units per day of the two kinds combined. What now is the optimal production plan?