The demand function for product X has been established, using regression analysis, as follows:

where Px, Pv, P, and Pw are the prices of products each identified by the subscript. The current price levels are as follows: PA = $188.50; Pv = $103.75; Pz = $119.25, and Pu, = $32.50.
The regression program also generated the following statistics: R2 — 0.92; Se = 80.01; Standard errors of the coefficients: for Pv, 8.62; for Pv, 33.91; for P-, 60.82; and for P„,, 35.82.

(a) What price would maximize sales revenue from the sale of product X?

(b) Suppose the marginal cost of producing X is constant at $100 per unit. What price would maximize profits from the sale of product X?

(c) Suppose the price of product Y is raised to $114.95. Does this increase have any impact on the profit-maximizing price for X? Explain.

(d) What qualifications and/or assumptions underlie your analysis?

Q = -5,154.605-35.83P 82.97 P, + 78.67P 64.03 P -