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 be described by C = $50,000 + 0.25Q, where C is total cost and Q is number of rolls (The high fixed costs represent development cost and tooling to prepare coating equipment). Night Timers' president seeks to establish a price that maximizes profit (since she is the chief stockholder). She thinks that the firm should be able to sell at least 125,000 rolls of tape per year.
(a) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only 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 estimated demand as given by Q = 350,000 - 200,000P is realized in the first year of production, should the company consider expanding capacity? Explain.

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The Answer of 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 be described by C = $50,000 + 0.25Q, where C is total cost and Q is number of rolls (The high fixed costs represent development cost and tooling to prepare coating equipment). Night Timers' president seeks to establish a price that maximizes profit (since she is the chief stockholder). She thinks that the firm should be able to sell at least 125,000 rolls of tape per year.
(a) If Night Timers plans to sell 125,000 rolls per year, what is the necessary price if the firm is to break even? What if it can only 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 estimated demand as given by Q = 350,000 - 200,000P is realized in the first year of production, should the company consider expanding capacity? Explain.

Night Timers Is a Small Company Manufacturing Glow-In-The-Dark Products