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

A

Explanation:

Answer 2

A

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=-(b)/(2a)`

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

`\displaystyle x=-((32))/(2(-4))=(32)/(8)=4`

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

Our answer is A.