A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be p = 10 − 42 D2 + 2D where p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. a) Derive how to find the number of units that should be produced annually to maximize profit. b) What is the maximum profit per year? c) What is the annual breakeven point? d) What is the company’s range of profitable output per year?
A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be p = 10 − 42 D2 + 2D where p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month. a) Derive how to find the number of units that should be produced annually to maximize profit. b) What is the maximum profit per year? c) What is the annual breakeven point? d) What is the company’s range of profitable output per year?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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A company produces and sells luxury goods and is able to control the demand for the product by varying the selling price. The relationship between price and demand is found to be
p = 10 − 42 D2 + 2D
where p is the price per unit in million dollars and D is the demand per year. The company is seeking to maximize its profit. The fixed cost is $59 million per year and the variable cost is $25 million per unit. The production capacity is 42 units per year, and the company produces at least 1 unit per month.
a) Derive how to find the number of units that should be produced annually to maximize profit.
b) What is the maximum profit per year?
c) What is the annual breakeven point?
d) What is the company’s range of profitable output per year?
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