Answer:
C(x) = 0.004x^2 + 90x + $8,500
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:
[tex]\int\limits {0.008x +90} \, dx = C(x) = \frac{0.008}{2}x^{2} +90 +C[/tex]
Where C is the constant or fixed costs
The equation above can be further solved as follows:
[tex]C(x) =0.004x^{2} +90x+C[/tex]
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
