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# Profit Maximizing order quantity

A television station is considering the sale of promotional dvds. It can have the dvds produced by one of two suppliers. Supplier A will charge the station a set-up fee of \$1200 plus \$2 for each dvds; supplier b has no set-up fee and will charge \$4 per dvd. The station estimates its demand for the dvds to be given by Q = 1600 - 200P, where p is the price in dollars and Q is the number of dvds. ( the price equation is P = 8 - Q/200.)

a. Suppose the station plans to give away the videos. How many dvds should it order? From which supplier?

b. Suppose instead that the station seeks to maximize its profit from sales of the dvds. What price should it charge? How many dvds should it order from which supplier? (hint: Solve two separate problems, one with supplier A and one with supplier B, and then compare profits. In each case, apply the MR=MC rule.)

#### Solution Preview

a. Suppose the station plans to give away the videos. How many dvds should it order? From which supplier?

Here P=0
Q=1600-200P
Q at P=0
Q=1600-200*0=1600
He should order 1600 dvds.

Suppose he orders from Supplier A,
Total cost=1200+2*1600=\$4400

Suppose he orders from Supplier B,
Total cost=4*1600=\$6400

Cost of ordering DVDs from supplier A is less. So, ...

#### Solution Summary

Solution describes the steps to find profit maximizing order quantity. It also determines the supplier at this level of order.

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