Respuesta :
We can write the cost function for UPS and FedEx depending on p (pounds).
UPS charges $7 for the first pound, and $0.20 for each additional pound. That means that there is a fixed cost and then a variable cost for every pound exceeding the first pound.
We can write this as:
[tex]C_{\text{ups}}=7+0.2(p-1)[/tex]The same happens for FedEx, but with different fixed and variable cost for the extra pounds:
[tex]C_{\text{FedEx}}=5+0.3(p-1)[/tex]We can calculate how many pounds will it take for both to cost the same by making both cost equal and solving for p:
[tex]\begin{gathered} C_{\text{ups}}=C_{\text{fedex}} \\ 7+0.2(p-1)=5+0.3(p-1) \\ 7-5=0.3(p-1)-0.2(p-1) \\ 2=0.1(p-1) \\ p-1=\frac{2}{0.1}=20 \\ p=20+1=21 \end{gathered}[/tex]At p=21 pounds, both services cost the same.
