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?

Question

Trystan Morrow

Mathematics

23 March, 19:03

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?

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Denisse Rocha · 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