Answer:
A
Step-by-step explanation:
The profit for selling x pairs of shoes is given by:
[tex]P(x)=-4x^2+32x-39[/tex]
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:
[tex]\displaystyle x=-\frac{b}{2a}[/tex]
In this case, a = -4, b = 32, and c = -39. Substitute and evaluate:
[tex]\displaystyle x=-\frac{(32)}{2(-4)}=\frac{32}{8}=4[/tex]
So, in order to maximize profit, only four pairs of sohoes should be sold.
Our answer is A.
