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.