The price p and the quantity x sold of a certain product obe

The price p and the quantity x sold of a certain product obey the demand equation p50, 0sxs 100 (a) 2 Express the revenue R as a function of x. (b) (c) (d) What is the revenue if 74 units are sold? What quantity x maximizes revenue? What is the maximum revenue? What price should the company charge to maximize revenue? (a) Express the revenue R as a function of x. R(x)-

Solution

p=(-1/2)x+50

Revenue,R(x)= px=((-1/2)x+50)x = (-1/2)x²+50x

b. R(74)= (-1/2)74²+50(74)=962

c. x=-b/2a= -50/2(-1/2)=50

R(50)=(-1/2)50²+50(50)=1250

d. p(50)=(-1/2)50 +50 =25