Question

A manufacturer believes that the cost function C(x)=52x2+85x+560 approximates the dollar cost of producing x units of a product. The manufacturer believes it cannot make a profit when the marginal cost goes beyond $270. What is the most units the manufacturer can produce and still make a profit? What is the total cost at this level of production?

Answer 1

$697

Explanation:

Marginal cost is the additional cost incurred as a result of increasing the number of items produced. Marginal cost is used to optimize production.

The marginal cost is gotten by differentiating the cost function, it is given by:

Marginal cost = C'(x)

The cost is given as C(x)=52x²+85x+560.

Given that the marginal cost should be less than $270, hence:

C'(x) < 270

104x + 85 < 270

104x < 270 - 85

104x < 185

x < 185/104

x < 1.77

Therefore x ≈ 1

C(1) = 52(1²) + 85(1) + 560 =

C(1) = $697