The Backus Corporation makes two products, X and Y. For every unit of

good X that the firm produces, it produces two units of good Y. Backus's total cost

function is

TC = 500 + 3Q + 9Q2(P.s. 9Q2 is 9Q to the power of 2)

where Q is the number of units of output (where each unit contains one unit of good

X and two units of good Y) and TC is total cost (in dollars). The demand curves for

the firm's two products are

PX = 400 - QX

PY = 300 - 3QY

where PX and QX are the price and output of product X and PY and QY are the price

and output of product Y.

(a) How much of each product should the Backus Corporation produce and sell per

period?

(b) What price should it charge for each product?