Question

The number of pounds of apples a cannery can process and the processing cost are P(h) = 375h and C(n) = 0.35n + 1000 where P(h) is the number of pounds of apples that can be processed in h hours and C(n) is the cost of processing n pounds of apples. Use composition of functions to find the cost of operating the cannery 32 hours. Be sure to show all of your work and the composed function you used

Answer 1

Given:

$\begin{gathered} P(h)=375h \\ C(n)=0.35n+1000 \end{gathered}$

The composition of function is:

$C(P(h))$

The value of C(P(h)) is:

$\begin{gathered} C(P(h))=0.35(375h)+1000 \\ =131.25h+1000 \end{gathered}$

Where h is denote time in hours then cost of operating in 32 hours that mean the value of h is 32 then:

$\begin{gathered} C(P(h))=131.25h+1000 \\ C(P(32))=131.25h+1000 \\ =131.25\times(32)+1000 \\ =4200+1000 \\ =5200 \end{gathered}$

So the final operating cost is 5200.