Question

The profit when selling 'x' pairs of shoes is P(x)=-4x^2+32x-39. How many pairs of shoes should be sold in order to maximize the profit
4 pairs
5 pairs
6 pairs
7 pairs

Answer 1

Answer:

A

Step-by-step explanation:

The profit for selling x pairs of shoes is given by:

$P(x)=-4x^2+32x-39$

And we want to determine the number of pairs that needs to be sold in order to maximize profit.

Since the function is a quadratic with a negative leading coefficient, the maximum profit will occur at its vertex point. The x-coordinate of the vertex of a quadratic is given by:

$\displaystyle x=-\frac{b}{2a}$

In this case, a = -4, b = 32, and c = -39. Substitute and evaluate:

$\displaystyle x=-\frac{(32)}{2(-4)}=\frac{32}{8}=4$

So, in order to maximize profit, only four pairs of sohoes should be sold.

Our answer is A.