Question

A company manufactures mountain bikes. The research department produced the marginal cost function Upper C prime​(x)equals700- x/ 3
​, 0 less than or equals x less than or equals 900​, where Upper C prime​(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 450 bikes per month to 900 bikes per month. Set up a definite integral and evaluate it.
The increase in cost is ​$
nothing.

Answer 1

Answer:

The increase in cost is     $C _{(900 - 450 )} =$ $ 213750      

Step-by-step explanation:

From the question we are told that

    The marginal cost function is  $C \ '(x) = 700 -\frac{x}{3}$   where $0 \le x \le 900$

     Since $C \ '(x)$ is in dollars it means that $C(x)$ is the cost price and x is given as  the number of bikes now to obtain $C(x)$  for the given increase of the  number of bikes we integrate $C\ '(x)$ within the increase limit

 This can be evaluated as

       $\int\limits^{900}_{450} {C \ '(x)} \, dx = \int\limits^{900}_{450} {700 - \frac{x}{3} } \, dx$

        $C(x) = [ {700x - \frac{x^2}{6} }] \left 900} \atop {450}} \right.$

         $C _{(900 - 450 )} = [700(900) - \frac{900^2}{6} ] - [700(450) - \frac{450^2}{6} ]$            

        $C _{(900 - 450 )} = 495000- 281250$      

      $C _{(900 - 450 )} =$ $ 213750