Question

A company manufactures mountain bikes. The research department produced the marginal cost function C'(x)=700-(x/3) where 0 is less than or equal to x which is less than or equal to 900. C'(x) is in dollars and x is the number of bikes produced per month. Compute the increase in cost going from a production level of 300 bikes per month to 900 bikes per month. Set up a definite integral and evaluate it.

Answer 1

Answer:

The increase in cost is $300,000.

Explanation:

The marginal cost function (C'(x)) is:

$C'(x) = 700 -\frac{x}{3}$

For 0≤ x ≤ 900.

Integrating the marginal cost function and evaluating it in the interval of 300 to 900 bikes, gives us the increase in cost of going from a production level of 300 bikes per month to 900 bikes per month:

$\int\limits^{900}_{300} {C'(x)}dx=\int\limits^{900}_{300} {(700 -\frac{x}{3})}dx\\C (x) = 700x - \frac{x^2}{6} +c\\ C(900) - C(300) = 700*900 - \frac{900^2}{6} +c - (700*300 - \frac{300^2}{6} +c)\\ C(900) - C(300) = 495,000 - 195,000\\C(900) - C(300) = 300,000$

The increase in cost is $300,000.