Posted by Elizabeth on .
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?

Mathematics in Economy 
Elizabeth,
I'd like to add that the '2' after x and y means 'squared'.