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.

Question

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? 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.

I cannot get this set up to work the problem can you help me?

Answer 1

a: if price is zero, then q=1600
how many to order is q.
then, cost to order from A is 1200+3200=4400
cost to order from b=4*1600=5200
order from A.
B: R=PQ-cost
dR/dq=dP/dq q + P- dCost/dq

now, for supplier A
dcost/dq=2

dR/dq=0=-1/200 q + 800-q/200 -2

q(1/100)=798
q= 79800

For supplier B
dR/dq=0=-q/200 +800-q/200 -4
q=79600

check that, it is late at night.

Answer 2

Thanks, bobpursely

Yes the B: R=PQ-cost is what I was missing at first, but after plugging it in and checking, it's correct. Thanks

You do great work when it's late!