Can someone please help me with Calculus, i have a test tomorrow?

its a Demand Equation: The price, p , and the quantity, x, sold of a certain product obey the demand equation

x= -20p+5000 and , p, is greater than or equal to 0 and less than or equal to 25

a.) Express the revenue R as a function of x.

b.) What is the revenue if 20 units are sold?

c.) Graph the revenue function using a graphing utility

d.) what quantity x maximizes revenue? What is the maximum revenue

e.)what price should the company charge to maximize revenue?

Top 1 Answers

A few days ago

fcas80

Favorite Answer

Quantity: x= -20p+5000

Price: p

a) Revenue = Quantity x Price = ( -20p+5000 )p =

-20p^2+ 5000p

b) -20(20^2) +5000(20) = 92000

d) dR/dx = -40p + 5000 = 0; p = 125.

Quantity = -20(125)+5000 = 2500

R = -20(125^2) +5000(125) = 312500

e) p =125

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