A television station is considering the sale of promotional DVDs. I can have the

Question

A television station is considering the sale of promotional DVDs. I can have the DVDs produced by one of two suppliers. Supplier A will charge the station a set-up fee of $1,200.00 plus $2.00 for each DVDs; supplier B has no set-up fee and will charge $4.00 per DVD. The station estimates its demand for the DVDs to be given by Q=1,600-20P, where P is the price in dollars and Q is the number of DVDs. (price equation is P=8-Q/200.)

a. Suppose the station plans to give away the video. 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.)

Explanation / Answer

a. If the station gives away the DVD's, the demand for the DVD's will be: Q = 1600 - 200P. At P = $0, The Quantity demanded (Q) will be 1600 units. This is the number that should be ordered. Supplier A will charge $1200 + 2*1600: $4,400 Supplier B will charge 4*1600: $6,400. Supplier A should get the order. b. To calculate the price that should be charged (and which supplier to order from) to maximize profits, we must calculate the maximum profit for each supplier we could choose. Marginal Profit = Marginal Revenue - Marginal Cost. Profit maximization occurs when Marginal Profit = 0, or when MR = MC. Supplier A: Revenue = Price * Quantity Cost = 1200 + 2*Q Q = 1600 - 200P P*Q=1200+2Q, when we substitute 1600 - 200P for Q, we get: P*(1600 - 200P) = 1200 +2(1600 - 200P). Solve for P. 1600P - 200P^2 = 1200 + 3200 - 400P 200P^2 -1600P - 400P +4400 = 0 P^2 - 10P +22 = 0, taking the first derivative of this yields the profit maximizing price dy/dx (first derivative) = 2P - 10 = 0, P = $5 = Profit Maximizing Price for Supplier A. At P = $5, we can now find our total profit... Demand = 1600 - 200*5 = 600 units. At D = 600, our revenue = 600*5 = $3,000 Cost = 1200 + 2*600 = $2,400 Profit = Revenue - Cost = $3000 - $2400 = $600 Supplier B: Revenue = Price * Quantity Cost = 4*Q Q = 1600 - 200P P*Q=4Q, when we substitute 1600 - 200P for Q, we get: P*(1600 - 200P) = 4(1600 - 200P). Solve for P. 1600P - 200P^2 = 6400 - 800P 200P^2 -2400P + 6400 = 0 P^2 - 12P +32 = 0 (if we solved this, we could also find the two points where profit = 0) dy/dx (first derivative) = 2P - 12 = 0, P = $6 = Profit Maximizing Price for Supplier A. At P = $6, we can find now find the maximum profit if we chose supplier B... Q = 1600 - 200*6 = 400 At Q = 400, and P = $6, Revenue = $2400 Cost = 400 * 4 = $1600 Profit = Revenue - Cost = $2400 - $1600 = $800 Since our maximum profit is greater with Supplier B, we should choose them, order 400 units, and charge $6/unit.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.