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# optimal output

The Staples 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 cureve for the finished product sold by the marketing division is Po=200-3Qo where Po is the price (in dollars per pound) of the finished product and Qo 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 TCo=100+15Qo where TCo 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?
C) What is the optimal transfer price for the basic plastic item?
D) At what price should the marketing division sell its product?

#### Solution Preview

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Question A
Demand function: Po=200-3Qo
P0Q = 200Q - 3Q^2
MR = 200 - 6Q

TCo=100+15Qo
MC = ...

#### Solution Summary

The marketing division's optimal output is computed.

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