A firm makes two products, x and y. Inverse demand for each shows that pricing in one market depends on sales in the other according to the equations:
Px = 1000 - 20x + 3y and Py = 500 - by + x.
The firm faces joint fixed cost of $12,000 and constant marginal cost of production in each product segment, MCX = $200, and MCV = $100.
a. What bundle of products (x*, y*) should the firm produce?
b. What prices will the firm be able to charge for each product given production at (x*, y*)?
c. What profits result in this instance?
d. At (x*, y*), what are the values of

Provide a short (one- or two-sentence) explanation for each value. That is, explain to your less mathematically sophisticated boss the economic significance of each value.
e. check your work by determining the profits that result if x and y are one unit more or less than optimal and fill in the following table

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