# Thread: Cost Function Involving Integrals

1. ## Cost Function Involving Integrals

The marginal cost function for a manufacturer's product is given by dc/dq = 10 - 100/(q+10) where c is the total cost in dollars when q units are produced. when 100 units are produced, the average cost is $50 per unit. to the nearest dollar, determine the manufacturer's fixed cost. There's no answer to this problem in my text. Here's my work so far. I'm not sure what to do next. Could someone demonstrate the remainder of the problem and solution? TC / q = AC TC/100=50 TC=5000 Finding integral of dc/dq gives c(q) = 10q - 100ln |q+10| Stuck at this part.. I tried this though: Let x be FC c(100) + x =5000 10(100)-100ln(100+10) + x = 5000 x=5000-529.95 x= 4 470.05 therefore FC is approx$4470

Is this correct?

2. $\displaystyle \int \frac{dc}{dq} ~dq \implies c(q) = 10q - 100\ln |q+10|+k$

$\displaystyle k$ is your fixed cost and you have $\displaystyle (q,c)=(100,5000)$ so

$\displaystyle c(100) = 10\times 100 - 100\ln |100+10|+k= 5000$

Now find $\displaystyle k$ .