Question

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

Answer 1

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