Flat Images develops and manufactures large, state-of-the-art flat-panel television screens that consumer electronic companies purchase and incorporate into a complete TV unit by adding the case, mounting brackets, tuner, amplifier, other electronics, and speakers. Flat Images has just introduced a new high-resolution, high-definition 60-inch screen. Flat Images is composed of two profit centers: Manufacturing and Marketing. Manufacturing produces sets that are sold internally to Marketing. Each profit center has the following cost structure: Manufacturing Marketing
Fixed cost (per month) $300,000 $150,000
Variable cost per screen $800 $200

Note that Marketing’s fixed cost of $150,000 and variable cost of $200 per screen do not contain any transfer price from Manufacturing. The numbers in the preceding table consist only of their own costs, not any costs transferred from the other department. The selling price that Marketing receives for each 60-inch screen depends on the number of screens sold that month, according to the following table:

An equivalent way to express the price-quantity relation in the table is P = $9,000 - 20Q, where P = price and Q = quantity.

Quantity Price
50 $8,000
75 7,500
100 7,000
125 6,500
150 6,000
175 5,500
200 5,000
225 4,500
250 4,000
275 3,500

Required:
a. Suppose that Manufacturing sets a transfer price for each screen at $4,800. How many screens will Marketing purchase to maximize Marketing’s profits (after Marketing pays Manufacturing $4,800 per screen) and how much profit will Marketing make?
b. At a transfer price of $4,800 per screen, and assuming Marketing buys the number of screens you calculated in part (a), how much profit is Manufacturing reporting?
c. At an internal transfer price of $4,800, and assuming Marketing purchases the number of screens you calculate in part (a), what is Flat Images’ profit?
d. Given the cost structures of Manufacturing and Marketing, and the price-quantity relation given in the problem, how many 60-inch screens should Flat Image manufacture and sell to maximize firmwide profits?