Question

A company that sells yoga mats estimates its annual profit using the equation below, where x represents the wholesale price in dollars of 1 yoga mat, and P = annual profit in thousands of dollars.

P = 10x? - 280x + 1,600 When the expression on the right side of this equation is factored completely, which best describes the meaning of the factors?
The annual profit is zero at a wholesale price of $80 and zero at a wholesale price of $200.
The annual profit is zero at a wholesale price of $8 and maximized at a wholesale price of $20.
The annual profit is zero at a wholesale price of $80 and maximized at a wholesale price of $200.
The annual profit is zero at a wholesale price of $8 and zero at a wholesale price of $20.

Answer 1

Answer: (d)

Explanation:

Given

Annual profit is given by

`P=10x^2-280x+1600`

When it is factored then,

`\Rightarrow 10x^2-280x+1600=0\\\Rightarrow 10\left( x^2-28x+160\right)=0\\\Rightarrow x^2-20x-8x+160=0\\\Rightarrow x(x-20)-8(x-20)=0\\\Rightarrow (x-8)(x-20)=0\\\Rightarrow x=8,20`

On factorization, we get that annual profit is zero at a whole prize of $8 and $20.