Suppose that the total cost of producing amounts x and y of two goods is TC = 3x + 4y - xy , and the prices (per unit) at which those amounts could be sold are px= 23 - x and py = 34 - y .

(a) Find profit as a function of output.

(b) Find the outputs of the two goods that give the maximum profit.

(c) How do you know that profits are at the maximum?