Night Timers is a small company manufacturing glow-in-the-dark products. One of

Question

Night Timers is a small company manufacturing glow-in-the-dark products. One of the hottest items the engineering department has developed is adhesive tape that can be applied to walls and floors. Night Timers chief engineer anticipates that the product will be sold in ten-foot rolls. At present, the company's maximum production capacity is 140,000 rolls per year. The engineer believes the cost function to b be described by C= $50,000 + 0.25Q..Night Timers president seeks to establish a price that maximizes profit. She thinks that the firm should be able to sell at least 125,000 rolls of tape per year. The marketing manager forecasts demand for the tape to be Q = 350,000 - 200,000P.
a.) If night timers plan to sell 125,000 rolls per year , what is the necessary price if firm is to break even? What if it can sell 100,000?
b.) The marketing manager forecasts demand for the tape to be: Q = 350,000 - 200,000P. Find the firm's profit maximizing output and price.
c.) If the demand forecast in part b is realized in the first year of production, should the company consider expanding capacity? Explain.

Explanation / Answer

Q = 350,000 – 200,000 P Q + 200,000 P = 350,000 P = 350,000 – Q P = 350,000/200,000 – Q/200,000 P = 1.75 – 0.000005 Q Profit = Revenue – Costs Profit = (P*Q) – ($50,000 + $0.25 Q) a) Q = 140,000 units b) P = 1.75 – 0.000005 Q P = 1.75 – (0.000005 * 140,000) P = 1.75 – 0.70 P = $1.05 C) Costs are $50,000 + $0.25 * 140,000 C = $50,000 + $35,000 C = $85,000 d) Revenue is quantity times price or 140,000 * $1.05 = $147,000 e) Profit = $147,000 – $85,000 = $62,000

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