Question 1096406
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The equation P(h) = 375h represents the number of pounds of apples that the cannery can produce. 


Saying 375h is the same as 375*h which means "375 times h"


The basic idea is that h represents the placeholder for any positive real number. For example, if h = 2, then 2 hours pass by and 375*h = 375*2 = 750 pounds of apples are processed.


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We can replace the P in P(h) = 375h with n to get n(h) = 375h. The n matches with the n in the other equation C(n) = 0.35n + 1000


Saying n(h) = 375h is the same as n = 375h


Since n = 375h, we can replace every copy of n in the second equation with 375h


C(n) = 0.35n + 1000


C(n) = 0.35*n + 1000


C(n) = 0.35*(n) + 1000


C(<font color=red>n</font>) = 0.35*(<font color=red>n</font>) + 1000


C(<font color=red>375h</font>) = 0.35*(<font color=red>375h</font>) + 1000 ... note how the n terms have been replaced with 375h


C(<font color=red>P(h)</font>) = 0.35*(375*h) + 1000 ... note how the 375h on the left side is replaced with P(h)


C(P(h)) = 0.35*(375*h) + 1000


C(P(h)) = (0.35*375)*h + 1000


C(P(h)) = 131.25*h + 1000


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Now plug in h = 32 


C(P(h)) = 131.25*h + 1000


C(P(<font color=red>h</font>)) = 131.25*<font color=red>h</font> + 1000


C(P(<font color=red>32</font>)) = 131.25*<font color=red>32</font> + 1000 ... every h is replaced with 32


C(P(32)) = 131.25*32 + 1000


C(P(32)) = 4200 + 1000


C(P(32)) = 5200


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Therefore the final answer is 5200 meaning that the total operating cost is $5,200 if you run the cannery for 32 hours.


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