Managerial Economics problem

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
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
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?

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