Answer:
The total monthly cost C(x) incurred by Carlota in manufacturing x guitars/month is C(x) = 0.004x^2 + 90x + 8,500.
Explanation:
Given,
C '(x) = 0.008x + 90 ................................... (1)
To obtain the the total monthly cost C(x) incurred by Carlota in manufacturing x guitars/month, we obtain the integral of equation (1) as follows:
[tex]C(x)=\int\limits {C'(x)} \, dx = \int\limits {[0.008x + 90]} \, dx[/tex]
C(x) = (0.008 / 2) x^2 + 90x + F
C(x) = 0.004x^2 + 90x + F .......................... (2)
Where F is the constant.
Since total cost is the addition of the total cost and total variable cost, the F in equation (2) represents the total fixed cost per month.
Since the fixed costs incurred by Carlota are $8500/month, this implies that F = 8,500.
Substituting F = 8,500 into equation (2), we have:
C(x) = 0.004x^2 + 90x + 8,500 <-------------- Total cost per month
Therefore, the total monthly cost C(x) incurred by Carlota in manufacturing x guitars/month is C(x) = 0.004x^2 + 90x + 8,500.
