Assignment 3: Television Station Instructions

Assignment 3assignment Instructionsa Television Station Is Considering

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,P, 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 DVDs 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. The textbook explains (P. 42-47) that maximum profit occurs where Marginal Revenue (MR) equals Marginal Cost (MC). Here, to find MR, you can refer to the inverse demand equation (P=a-bQ). The marginal cost (MC) is what each supplier charges to produce an additional DVD, directly deduced from the given cost equations. If uncertain, calculate the cost for 1 DVD and 2 DVDs; the difference is the marginal cost.

Complete this assignment in a Microsoft Word document, APA formatted, and submit it as Assignment 3 by midnight, Day 7. Show and explain your work. The assignment is primarily mathematical, so length is flexible.

Paper For Above instruction

The decision-making process for a television station contemplating the sale or giveaway of promotional DVDs involves a complex balance of cost analysis, demand estimation, and profit maximization strategies. The two scenarios—giving away DVDs versus selling them—necessitate distinct analytical approaches. Here, we explore both cases with a detailed calculation process based on the given demand functions and cost structures, culminating in recommendations on the optimal quantity and price points from either supplier.

Scenario A: Giving Away DVDs

In the case where the station intends to give away the DVDs, the primary consideration is the quantity that maximizes reach without incurring costs that outweigh the benefits. The demand function is specified as Q = 1, P, with the price equation P = 8 - Q/200. When DVDs are given away free of charge, the implicit price P is zero; thus, solving for Q at P=0 yields Q = 8 200 - (Q/200)200, simplifying to find the quantity.

Substituting P=0 into the demand equation: 0 = 8 - Q/200, which simplifies to Q = 8200 = 1600 DVDs. Given this demand level, the station needs to determine which supplier offers the most cost-effective way to produce these DVDs. Supplier A's cost per DVD is $2 with a $1200 setup fee, totaling $1200 + 2Q. For Q=1600, total cost = 1200 + 21600 = $1200 + $3200 = $4400. Supplier B's total cost is $4 per DVD times 1600 DVDs, totaling $4*1600 = $6400. Therefore, between the two, Supplier A is more economical at this quantity.

Scenario B: Profit Maximization

When the station aims to maximize profit through sales, it must determine the optimal price and quantity that equate marginal revenue with marginal cost for each supplier. The inverse demand function is P = 8 - Q/200, which forms the basis for calculating total revenue (TR) as TR = P*Q = (8 - Q/200)Q = 8Q - Q²/200. To find MR, the derivative of TR with respect to Q is needed; however, since calculus is restricted, MR can be approximated by considering the change in TR with small changes in Q.

Alternatively, following the steps from the textbook (P. 44), MR can be derived from the inverse demand function: MR = a - 2bQ, where, in this case, a=8 and b=1/200. Substituting, MR = 8 - 2(1/200)Q = 8 - Q/100.

Next, the marginal cost (MC) for each supplier is considered. Supplier A's MC per DVD is \$2, and the setup fee is irrelevant for marginal analysis (as it is a fixed cost). For Supplier B, with a per DVD cost of \$4, the MC is \$4.

Setting MR equal to MC for Supplier A: 8 - Q/100 = 2, which yields Q = (8-2)100 = 6100 = 600 DVDs. From this quantity, the price can be determined from the demand equation: P = 8 - (Q/200) = 8 - (600/200)= 8 - 3= \$5. For Supplier A, the profitable quantity is 600 DVDs at a price of \$5 each.

Similarly, for Supplier B, MR=MC: 8 - Q/100 = 4, solving for Q: Q = (8-4)100 = 4100 = 400 DVDs. The corresponding price at Q=400 is P= 8 - (400/200)= 8-2= \$6.

Calculating total profit for each supplier involves subtracting total costs from total revenue:

• Supplier A: TR = \$5 600 = \$3000; Total Cost = 1200 + 2600 = \$1200 + \$1200= \$2400; Profit = \$3000 - \$2400= \$600.
• Supplier B: TR = \$6 400= \$2400; Total Cost = 4400= \$1600; Profit= \$2400 - \$1600= \$800.

Therefore, the station maximizes profit from sales by producing 400 DVDs in bulk from Supplier B at a unit price of \$6, resulting in a profit of \$800, which exceeds the profit from Supplier A.

In summary, for giving away DVDs, choosing the supplier with the lowest total cost at that volume—Supplier A—is optimal. For sales, the profit-maximizing strategy involves producing 400 DVDs from Supplier B at \$6 each. This analysis illustrates how different objectives (distribution vs. profit maximization) significantly influence strategic decisions regarding pricing and supplier selection.

Conclusion

The two scenarios highlight the importance of understanding demand functions, cost structures, and the principles of revenue and profit maximization in business decision-making. When giving away DVDs, the focus is on volume rather than revenue, favoring the supplier with lower total costs at high volumes. Conversely, when seeking profit, aligning marginal revenue with marginal cost guides the optimal quantity and pricing strategy. These insights demonstrate the crucial role of economic analysis in making informed operational decisions.

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