Answer:
Price of pair of socks should be $5
Step-by-step explanation:
The question is asking: "What sock price should the company set to earn a maximum profit?"
The equation is given as:
[tex]P(x)=-3(x-5)^2+12[/tex]
This is a quadratic equation given in vertex form which is:
[tex]f(x)=a(x-b)^2+c[/tex]
Where
(b,c) is the vertex and it means that maximum of the function occurs at x = b and the maximum value is "c"
In the context of the question:
Max is 12 and it occurs at x = 5
So, they should set the price of socks at $5 to earn a profit (max) of $12 million
