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
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?