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Finding the optimal price and output combination

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 $1,200 plus $2 for each DVD; supplier B has the no set-up fee and will charge $4 per DVD. The station estimates its demand for the DVDs to be given by Q = 1,600 - 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 stations seek to maximize its profits from sales of the DVDs. What price should it charge? How many DVDs should it order from which supplier?

Solution Preview

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

Q=1600-200P
Let us calculate the number of DVDs needed at nil price i.e. 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 ...

Solution Summary

It is very important to choose an optimal price and output combination in the day to day business. Solution to given problem depict the steps to determine the optimal price and output combination with the help of given equation.

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