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

Question

The price p and the quantity x sold of a certain product obey the demand equation below. x3p +66, 0sps 22 (a) Express the revenue R as a function of x (b) What is the revenue if 60 units are sold? (c) What quantity x maximizes revenue? What is the maximum revenue? (d) What price should the company charge to maximize revenue? (e) What price should the company charge to earn at least $288 in revenue? (b) The revenue if 60 units are sold is $ (Simplify your answer.) (c) The quantity units maximizes revenue (Simplify your answer.) The maximum revenue is $ (Simplify your answer.) (d) The company should charge $to maximize revenue. (Simplify your answer.) (e) The company should charge at least Sto at most Sto earn at least $288 in revenue.

Explanation / Answer

x = -3p +66

3p =66-x

p =22 -(1/3)x

a)

R(x) =x*p

=22x -(1/3)x²

b)

R(60) = 22*60 -1/3 *60^2

=$ 120

c)

x = -b/2a

= -22/(2 *(-1/3))

= 33 units

maximum revenue is

R(33) = $363

d)

p(33) =22 -(1/3)*33

=$11

e)

At least $18 and at most $48

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