Write a mathematical expression for the function to generate daily costs;fixed running cost $60 per dayEach belt made $3 (max 50 per day)What is...

`f(x) = 3x + 60`

Domain `{x
in NN|xlt=50}`or `{0,1,2,...,50}`

Range `{y in NN|x in NN,
x<=50,y=3x+60}`or
`{60,63,66,69,...,207,210}`

Inverse:

(1)First
replace f(x) with y to get

` y =
3x+60`

(2)Exchange x and y to
get

` x = 3y +
60`

(3)Solve for
y

`y =
1/3x-20`

`f^(-1)(x)=1/3x-20`

Domain
is {60, 63, 66, 69,...,207,210}

Range is
{0,1,2,...,50}

The inverse would allow us to target a given
cost and find the number of belts we would have to make to generate that cost.  So if
you want a cost of 120, we could put it into the inverse function and find we have to
make 20 belts.

The manufacturer could use the cost function
along with a profit function to determine the optimum number of belts to make to
maximize profit.  They could also use this to determine the price they should sell an
item at in order to optomize their profit.

So the answers
are:

`f(x)=3x+60` Domain {0,1,...50}, Range
{60,63,66,...,207,210}

`f^(-1)(x)=1/3x-20` Domain
{60,63,66,...,207,210}, Range {0,1,2,...,49,50}