Group Problem 4

The price p and the quantity x sold of a certain product obey the demand equation below

x = -2 p + 52; 0< or =p< or =30

(a) Express the revenue R as a function of x ( R = xp ).

(b) What is the revenue if 38 units are sold?

(c) What quantity x maximizes revenue?

(d) What is the maximum revenue?

(e) What price should the company charge to maximize revenue?

(f) What price should the company charge to earn at least $288 revenue?

Challenge: Notice that if the price is $0 or $26 the revenue is $0. It is easy to explain why revenue would be $0 if the price is $0, but how can revenue be $0 if the price is $26?