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