# Find a linear cost function

First, I can find a cost function where fixed cost is involved.

• Eight units cost $\$300$; fixed cost is$\$60$.

I got $C(x)= 30x + 60$

However, for a problem like

• Twelve units cost $\$445$;$50$units cost$\$1585$.

I don't think my solution process is right. I get the slope like always, which is $30$, and create the $C(x)$ from one of the points \begin{align*} p-445 & = 30(q-12)\\ p-445 & = 30q-360\\ p & = 30q + 85\\ C(x)& = 30x+85 \end{align*}

Now, the solution says the function I've created is wrong. Can anyone tell me what I'm doing wrong?

• Your solution is correct. There is an error in the solution key. – N. F. Taussig Jun 9 '17 at 10:41

Slope should be $\frac{1585-445}{50-12}=\frac{1140}{38}=\$30$per unit. Now point slope,$p-445=30(q-12)p-445=30q-360p=30q+85C(x)=30x+85\$
• For the first one, we have a slope of $$\frac{300 - 60}{8} = \frac{240}{8} = 30$$ You forgot to take into account the fixed costs. – N. F. Taussig Jun 9 '17 at 10:33