Question

A manufacturer finds that the revenue generated by selling x units of a certain commodity is given by the function R(x) = 60x − 0.2x2, where the revenue R(x) is measured in dollars. What is the maximum revenue, and how many units should be manufactured to obtain this maximum?

Answer 1

R(x) = 60x - 0.2x^2

The revenue is maximum when the derivative of R(x) = 0.
dR(x)/dx = 60 - 0.4x = 0
0.4x = 60
x = 60/0.4 = 150

Therefore, maximum revenue is 60(150) - 0.2(150)^2 = 9000 - 4500 = $4,500
Maximum revenue is $4,500 and the number of units is 150 units

Answer 2

Answer:

Revenue for a new product sold by your company is given by the function R(x) = −0.05x2 + 60x. Use the function to calculate the maximum revenue of the product.

A) $14,000  

B) $16,000  

C) $18,000  

D) $20,000

Step-by-step explanation:  THE answer is C