Question

(1 point) an advertiser goes to a printer and is charged $43 for 80 copies of one flyer and $54 for 218 copies of another flyer. the printer charges a fixed setup - cost plus a charge for every copy of the flyer. find a function that describes the cost of a printing job, if $n$ is the number of copies made. (you must either use fractions or numbers with 3 decimal places of accuracy) $c(n)=$ you have attempted this problem 0 times. you have unlimited attempts remaining. email instructor

Explanation:

Step1: Set up a system of equations

Let the fixed - setup cost be $b$ and the cost per copy be $m$. We have the following two equations based on the given information:
When $n = 80$, $C(80)=80m + b=43$. When $n = 218$, $C(218)=218m + b=54$.

Step2: Subtract the first equation from the second

$(218m + b)-(80m + b)=54 - 43$. This simplifies to $218m+ b - 80m - b=11$, and further to $138m = 11$. Then $m=\frac{11}{138}\approx0.07971$.

Step3: Find the value of $b$

Substitute $m=\frac{11}{138}$ into the first equation $80\times\frac{11}{138}+b = 43$.
$b=43-\frac{880}{138}=43 - 6.37681\approx36.623$.

Step4: Write the cost - function

The cost function $C(n)$ is of the form $C(n)=mn + b$. Substituting $m=\frac{11}{138}$ and $b = 43-\frac{880}{138}$, we get $C(n)=\frac{11}{138}n+43-\frac{880}{138}\approx0.07971n + 36.623$.

Answer:

$C(n)=0.080n + 36.623$