solution

The Xerxes Company is composed of a marketing division and a production

division. The marketing division packages and distributes a plastic item made

by the production division. The demand curve for the finished product sold

by the marketing division is P0 = 200 – 3Q0

where P0 is the price (in dollars per pound) of the finished product and Q0 is

the quantity sold (in thousands of pounds). Excluding the production cost of

the basic plastic item, the marketing division’s total cost function is

TC0 = 100 + 15Q0 where TC0 is the marketing division’s total cost (in thousands of dollars). The

production division’s total cost function is TC1 = 5 + 3Q1 + 0.4Q1

2 where TC1 is total production cost (in thousands of dollars) and Q1 is the total

quantity produced of the basic plastic item (in thousands of pounds). There

is a perfectly competitive market for the basic plastic item, the price being

$20 per pound. a. What is the optimal output for the production division?

b. What is the optimal output for the marketing division?