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An advertiser goes to a printer and is charged $45 for 90 copies of one flyer and $50 for 216 copies of another flyer. The printer charges afixed setup cost plus a charge for every copy of single-page Ayers. Find a function that describes the cost of a printing job, if « is thenumber of copies made. C(x) =Submit answer

Respuesta :

Given:

[tex]\begin{gathered} C(x)=\cos t\text{ for x copies} \\ F=\text{fixed setup cost} \\ P=\text{ per copy charge} \end{gathered}[/tex]

so the cost of x copies is:

[tex]C(x)=F+Px[/tex]

One flyer is

[tex]\begin{gathered} C(x)\colon\cos t=45 \\ \text{Number of copy (x)=90} \end{gathered}[/tex]

so equation is:

[tex]\begin{gathered} C(x)=F+Px \\ 45=F+P\times(90) \\ F=45-90P \end{gathered}[/tex]

Another flyer is:

[tex]\begin{gathered} C(x)\text{ cost=50} \\ x\text{ Number of copies= 216} \end{gathered}[/tex][tex]\begin{gathered} C(x)=F+Px \\ 50=F+P(216) \\ F=50-216P \end{gathered}[/tex]

For F put the all value is equal.

[tex]\begin{gathered} 45-90P=50-216P \\ 216P-90P=50-45 \\ 126P=5 \\ P=\frac{5}{126} \\ P=0.0396 \end{gathered}[/tex]

Put the value of P for F

[tex]\begin{gathered} F=50-216P \\ F=50-216(0.0396) \\ F=50-8.5536 \\ F=41.4464 \end{gathered}[/tex]

So the function of C(x) is:

[tex]\begin{gathered} C(x)=F+Px \\ C(x)=41.4464+0.0396x \end{gathered}[/tex]

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