Posted by **Elizabeth** on Monday, January 18, 2010 at 3:28pm.

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) = 0.04x2 + 0.01xy + 0.01y2 +4x + 2y +500

Suppose that firm sells all its output at a price per unit of 15 for A and 9 for B.

Find the daily production levels x and y that maximise profit per day.

Suppose that any production by the firm creates pollution, so it is legally restricted to produce a total of 320 units of the two kinds of output. What now are the optimal quantities of the two kinds of output?

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