Question

The cost in dollars to produce x shovels in a factory is given by the function C(x)=33x+430. The number of shovels that can be produced in h hours is given by the function N(h)=30h

7. Find the rule for​ C(N(h)).
8. Find the cost when h=12 hours

Answer 1

Okay, to find the maximum number of shovels that can be produced with $10,000, we need to do the following:

1) Set the cost function C(N(h)) = 10,000. So: 990h + 430 = 10,000

2) Subtract 430 from both sides: 990h = 9,570

3) Divide both sides by 990: h = 9.75 (round to 10 hours)

4) Substitute 10 hours into the function for number of shovels:

N(10) = 30(10) = 300 shovels

Therefore, the maximum number of shovels that can be produced with $10,000 is 300 shovels.

Let me know if you have any other questions!