Question

The cost, C, to produce b baseball bats per day is modeled by the function C(b) = 0.06b2 – 7.2b + 390. What number of bats should be produced to keep costs at a minimum?

Answer 1

Answer: 60

I got it correct on my quiz :)

Answer 2

Number of bats should be produced to keep costs at a minimum is 60.

Explanation:

Given : The cost, C, to produce b baseball bats per day is modeled by the function
`C(b) = 0.06b^2 -7.2b + 390`.

To find : What number of bats should be produced to keep costs at a minimum?

Solution :

Function in quadratic form is
`C(b) = 0.06b^2 -7.2b + 390`

To determine the minimum point we apply the formula of quadratic equation
`ax^2+bx+c=0` is
`x=-(b)/(2a)`

On comparing with given model, a=0.06 , b=-7.2 , c=390

The minimum point is at
`b=-(-7.2)/(2(0.06))`

`b=-(-7.2)/(0.12)`

`b=(7.2)/(0.12)`

`b=60`

i.e. The minimum number of bats per day is 60.

The cost at b=60 is

`C(60) = 0.06(60)^2 -7.2(60) + 390`

`C(60) = 216 -432 + 390`

`C(60) =174`

The minimum cost is $174 and minimum number of bats is 60.

We can also determine through graph.

Refer the attached figure below.