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?
