Question

The profit that the vendor makes per day by selling x pretzels is given by the function. P(x) = -0.002x2 + 1.4x - 400. Find the number of pretzels that must be sold to maximize profit.

Answer 1

350 the number of pretzels that must be sold to maximize profit.

Step-by-step explanation:

P(x) = -0.002x2 + 1.4x - 400

Differentiating P(x) with respect to dx:

`P(x)'=(d(-0.002x2 + 1.4x - 400))/(dx)`

`P(x)'=-2* 0.002x+1.4`

Putting , P(x)' =0

`0=-0.004x+1.4`

`x=(1.4)/(0.004)=350`

we get , x = 350

Differentiating P(x)' with respect to dx:

`P(x)''=-0.004`

P(x)''<0 (maxima)

350 the number of pretzels that must be sold to maximize profit.