Write down the revenue function, cost function, and profit function as functions of p. How much should she charge per glass to maximize her profit? What is the maximum profit?

Economics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter20: Consumer Choice And Elasticity
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Elsie sells homemade lemonade. If she prices a glass of lemonade at $3, she sells 12 glasses a day. If she gives a $0.50 discount (per glass), she can sell 3 more glasses per day.

Write a linear demand equation

q = mp + b,

where p is the price per glass, and q is the number of glasses she can sell per day.

Suppose that it costs her 20 cents a glass to make lemonade. There is no fixed cost.

Write down the revenue function, cost function, and profit function as functions of p. How much should she charge per glass to maximize her profit? What is the maximum profit?

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