Question

The daily profit, P(x), of an oil refinery is given by P(x) = 8x -0.02x², where x is the

number of barrels of oil refined.

a. How many barrels should be refined to maximize the profit?

b. What is the maximum profit?

Answer 1

Answer: a. To find the number of barrels that should be refined to maximize profit, we need to find the critical point of the function P(x), which occurs where the derivative of P(x) equals zero.

P(x) = 8x - 0.02x²

P'(x) = 8 - 0.04x

Setting P'(x) = 0, we get:

8 - 0.04x = 0

Solving for x, we get:

x = 200

Therefore, 200 barrels should be refined to maximize the profit.

b. To find the maximum profit, we substitute x = 200 into the profit function P(x):

P(200) = 8(200) - 0.02(200)²

P(200) = 1600 - 800

P(200) = 800

Therefore, the maximum profit is $800.

Explanation: