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 is
P_0=200-3Q_0
Where P_0 is the price (in dollars per pound) of the finished product and Q_0 is the quantity sold
(in thousands of pounds). Excluding the production cost of the basic plastic item, marketing division's total cost function is TC_0=100+15Q_0
Where TC_0 is the marketing division's total cost (in thousands of dollars). The production division's total cost function is TC_1=5+3Q_1 + 0.4Q_1^2
Where TC_1 is total production cost (in thousands of dollars) and Q_1 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?