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

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 DVD; 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 = 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 station seeks to maximize its profit from sales of DVDS. What price should be charged? How many DVD should it order from which supplier?
Directions: You must solve two separate problems, one with supplier A and one with supplier B, and then compare profits. As the textbook explains (P. 42-47), maximum profit is found where Marginal Revenue (MR) to Marginal Cost (MC). Here, you need to set MR=MC for each supplier and compare the maximum profit attainable for each.

Calculating marginal products can be challenging. Here is one way to do it without using calculus.

To calculate MR, you can look at the bottom of page 44 in the book. It shows how to get it from the inverse demand equation (P=a-bQ).

The marginal cost (MC) is what each supplier charges to produce an extra DVD. This can be directly deduced from the text of the homework (the equations provided for the cost of suppliers). If you are not sure, one easy way is to calculate the cost for 1 DVD and the cost for 2 DVD. The difference would be the marginal cost.

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