The question is incomplete. The complete question is :
A manufacturer of mountain bikes has the following marginal cost function:
[tex]$C'(q)=\frac{700}{0.7q+8}$[/tex]
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 $200 each, what is the profit (or loss) on the first 30 bikes?
Solution :
Given :
[tex]$C'(q)=\frac{700}{0.7q+8}$[/tex]
a). Fixed cost, FC = $ 2800
Total cost to produce 30 bicycles is :
[tex]$C = 2800 + \int_0^{30} C'(q) \ dq$[/tex]
[tex]$ = 2800 + \int_0^{30} \frac{700}{0.7q+8} \ dq$[/tex]
[tex]$= 2800+700\left[\frac{\ln (0.7q+8)}{0.7}\right]^{30}_0$[/tex]
[tex]$=2800+1000[\ln ((0.7 \times 30)+8)- \ln 8 ]$[/tex]
[tex]$= 2800 +1000 [\ln 29 - \ln 8]$[/tex]
= 2800 + 1287.85
= $ 4087.85
b). Total selling price = $ (200 x 30)
= $ 6000
Profit = 6000 - 4087.85
= $ 1912.15
