A liquid form of penicillin manufactured by a pharmaceutical firm is sold in bulk at a price of

$200 per unit. If the total production cost (in dollars) for x units is

C (x) = 500,000 + 80x + 0.003x^2

and if the production capacity of the firm is at most 30,000 units in a specfied time, how many

units of penicillin must be manufactured and sold in that time to maximize the profit?

Question

Mia Greene

Mathematics

31 March, 19:42

A liquid form of penicillin manufactured by a pharmaceutical firm is sold in bulk at a price of

$200 per unit. If the total production cost (in dollars) for x units is

C (x) = 500,000 + 80x + 0.003x^2

and if the production capacity of the firm is at most 30,000 units in a specfied time, how many

units of penicillin must be manufactured and sold in that time to maximize the profit?

+2

Answers (1)

Know the Answer?

Everett Merritt · Answer 1

The revenue is given by the unit price * number of units.

Profit = Revenue - Cost = 200x - 500,000 - 80x - 0.003x^2 = 120x - 500,000 - 0.003x^2

For profit to be maximum dP/dx = 0

120 - 0.006x = 0

x = 120/0.006 = 20,000

Therefore, to maximize profit, the firm should produce 20,000 penicillin.