Chapter 5.5, Problem 70E

Cost. Referring to Problem 69, compute the increase in cost going from a production level of 0 bikes per month to 600 bikes per month. Set up a definite integral and evaluate it.

69. Cost. A company manufactures mountain bikes. The research department produced the marginal cost function

     $\begin{array}{cc}{C}^{\prime }\left(x\right)=500-\frac{x}{3}& 0\le x\le 900\end{array}$

where 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.