Question

The cost c, to produce b baseball bats per day is modeled by the function c(b)=0.06b^2 - 7.2b + 390. What number of bats should be produced to keep costs at a minimum?

Answer 1

You have two choices.
The minimum possible cost to operate your bat factory for a day is $390,
and there are two quantities of bats that both cost that much.

One possibility: 
                   Produce no bats at all per day.  Zero.  Nada.  None.
                   Cost = 0.06(0)²  -  7.2(0)  +  390  =  $390 per day.

The other choice:
                   Produce  120 bats per day.
                   Cost = 0.06(120²)  -  7.2(120)  +  390
                          = 0.06(14,400)  -  7.2(120)  +  390
                          =      864          -      864      +  390
                          =      $390  per day.

If you produce any other number of bats in a day ... more than zero
but not 120 ... then it will cost you more than $390 to operate the factory
that day.