When the price of a glass of lemonade at lemonade stand was $1.75, 400 glasses were sold. Assume that the demand function is linear and that the marginal and fixed cost are $0.10, and $25 respectively

AFind the profit p as a function of x, the number of glasses of lemonade sold

B Use graphing utility to graph p and comment about slopes of P when X=300 and X=700

C Find the marginal profit when 300 glasses are sold and when 700 of lemonade glasses are sold

Question

Mathematics

Spears

13 April, 04:59

When the price of a glass of lemonade at lemonade stand was $1.75, 400 glasses were sold. Assume that the demand function is linear and that the marginal and fixed cost are $0.10, and $25 respectively

AFind the profit p as a function of x, the number of glasses of lemonade sold

B Use graphing utility to graph p and comment about slopes of P when X=300 and X=700

C Find the marginal profit when 300 glasses are sold and when 700 of lemonade glasses are sold

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Answers (1)

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Alessandro Dickson · Answer 1

Step-by-step explanation:

A. Price is 1.75

Total revenue, if number of galsses equals X is 1.75X

Total cost function of X glasses of lemonade is 25+0.1X

Profit function is Revenue - Cost, P=1.75X-25-0.1X=1.65X-25

C. Marginal profit = d/dx (1.65x-25) = 1.65-0=1.65

X=300 glasses, P' (300) = 1.65

X=700 glasses, P' (700) = 1.65