The number of pounds of apples a cannery can produce 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.

number of apples processed

= P(22) = .... do the arithmetic

cost = C(P(22)) = put the answer of P(22) into C(n)

To find the cost of operating the cannery for 32 hours, we need to use the composition of functions, which means plugging the output of one function into another.

First, let's find the number of pounds of apples that can be processed in 32 hours. We use the function P(h) = 375h, where P is the number of pounds of apples that can be processed in h hours:

P(32) = 375 * 32
P(32) = 12,000 pounds

Now that we know the number of pounds of apples that can be processed in 32 hours, we can find the cost using the function C(n) = 0.35n + 1000, where C is the cost of processing n pounds of apples:

C(12,000) = 0.35 * 12,000 + 1000
C(12,000) = 4,200 + 1000
C(12,000) = 5,200

Therefore, the cost of operating the cannery for 32 hours is $5,200.