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.
C(n) = C(P(h))
= .35P(h)+1000
= 0.35(375h)+1000
To find the cost of operating the cannery for 32 hours, we need to find the composition of functions C(P(h)).
First, let's find the number of pounds of apples that can be processed in 32 hours, which is represented by P(32).
P(h) = 375h
P(32) = 375 * 32
= 12,000 pounds
Now, we can substitute this value into the C(n) function to find the cost of processing 12,000 pounds of apples.
C(n) = 0.35n + 1000
C(12,000) = 0.35 * 12,000 + 1000
= 4,200 + 1000
= 5,200
Therefore, the cost of operating the cannery for 32 hours is $5,200.
To find the cost of operating the cannery for 32 hours, we need to use the composition of functions.
The composition of functions involves taking the output of one function and using it as the input for another function.
Here, we have two functions: P(h) represents the number of pounds of apples that can be processed in h hours, and C(n) represents the cost of processing n pounds of apples.
We want to find the cost of operating the cannery for 32 hours, so we need to find C(P(32)).
Step 1: Find P(32)
To find P(32), we substitute 32 for h in the equation P(h) = 375h:
P(32) = 375(32)
P(32) = 12000
Step 2: Find C(P(32))
Now that we know P(32) is 12000, we can substitute it into the equation C(n) = 0.35n + 1000:
C(P(32)) = 0.35(12000) + 1000
C(P(32)) = 4200 + 1000
C(P(32)) = 5200
Therefore, the cost of operating the cannery for 32 hours is $5200.