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

Answer:

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

Explanation:

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

Differentiating P(x) with respect to dx:

$P(x)'=\frac{d(-0.002x2 + 1.4x - 400)}{dx}$

$P(x)'=-2\times 0.002x+1.4$

Putting , P(x)' =0

$0=-0.004x+1.4$

$x=\frac{1.4}{0.004}=350$

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.