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 + 0.4Q12
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?
c. What is the optimal transfer price for the basic plastic item?
d. At what price should the marketing division sell its product?