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?

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.