Question

A manufacturer estimates that the profit from producing ? refrigerators per day is ?(?) = −8?^2 + 320? dollars. What is the largest possible daily profit?

Answer 1

Step 1)

we have,

Hence,

equate it to 0 we can say that,

Hence we can say that x = 20 is the critical point of profit function

we have,

Hence,

Hence,

As P''(20) = -16 < 0 according to second derivative test we can say that x = 20 is a maximum point

Hence we can say that profit is maximum at x = 20

Step 2)

we have,

Put x = 20 we can write,

Hence we can say that largest possible daily profit is $3200