Question

When calculating the marginal revenue and marginal profit in this problem, use the approach given for the marginal cost and marginal revenue in the discussions in your textbook. a) If the fixed cost in producing the bicycles is $2800, find the total cost to produce 30 bicycles. Answer: $ 4718.9869 equation editorEquation Editor b) If the bikes are sold for $200 each, what is the profit (or loss) on the first 30 bikes

Answer 1

The question is incomplete. The complete question is :

A manufacturer of mountain bikes has the following marginal cost function:

                                           $C'(q)=\frac{700}{0.7q+8}$

where q is the quantity of bicycles produced.

When calculating the marginal revenue and marginal profit in this problem, use the approach given for the marginal cost and marginal revenue in the discussions in your textbook.

a) If the fixed cost in producing the bicycles is $2800, find the total cost to produce 30 bicycles?

b) If the bikes are sold for $200 each, what is the profit (or loss) on the first 30 bikes?

Solution :

Given :

$C'(q)=\frac{700}{0.7q+8}$

a). Fixed cost, FC = $ 2800

Total cost to produce 30 bicycles is :

 $C = 2800 + \int_0^{30} C'(q) \ dq$

      $= 2800 + \int_0^{30} \frac{700}{0.7q+8} \ dq$

     $= 2800+700\left[\frac{\ln (0.7q+8)}{0.7}\right]^{30}_0$

     $=2800+1000[\ln ((0.7 \times 30)+8)- \ln 8 ]$

     $= 2800 +1000 [\ln 29 - \ln 8]$

    = 2800 + 1287.85

    = $ 4087.85

b). Total selling price = $ (200 x 30)

                                   = $ 6000

    Profit  =  6000 - 4087.85

                = $ 1912.15