Question

Carlota Company estimates that the marginal cost of manufacturing its Professional Series guitars is given by the following in dollars/month when the level of production is x guitars/month.

C '(x) = 0.008x + 90

The fixed costs incurred by Carlota are $8500/month. Find the total monthly cost C(x) incurred by Carlota in manufacturing x guitars/month.

Answer 1

C(x) = 0.004x^2 + 90x + $8,500

Step-by-step explanation:

In order to find the to monthly cost C(x) incurred, the marginal cost C '(x) = 0.008x + 90 will have to be integrated using integral calculus as follows:

`\int\limits {0.008x +90} \, dx = C(x) = (0.008)/(2)x^(2) +90 +C`

Where C is the constant or fixed costs

The equation above can be further solved as follows:

`C(x) =0.004x^(2) +90x+C`

Since fixed costs is $8500/month, we substitute for C to obtain the the total monthly cost C(x) incurred by Carlota in manufacturing x guitars/month as follows:

C(x) = 0.004x^2 + 90x + $8,500