select the correct answer from each drop - down menu.\nfunction p models the weekly profit, $p(x)$, a…

select the correct answer from each drop - down menu.\nfunction p models the weekly profit, $p(x)$, a clothing company earns for making and selling $x$ jackets.\n$p(x)=-0.0005(x^{2}+30)(x - 20)(x - 70)$\nconsider the graph of function p.\nthe companys profit will be exactly $0 if it makes and sells \njackets. the company will make a profit if it makes and sells \njackets, but will not make a profit if it makes and sells \njackets.

select the correct answer from each drop - down menu.\nfunction p models the weekly profit, $p(x)$, a clothing company earns for making and selling $x$ jackets.\n$p(x)=-0.0005(x^{2}+30)(x - 20)(x - 70)$\nconsider the graph of function p.\nthe companys profit will be exactly $0 if it makes and sells \njackets. the company will make a profit if it makes and sells \njackets, but will not make a profit if it makes and sells \njackets.

Answer

Explanation:

Step1: Find when profit is $0

Set $P(x)=0$. Since $P(x)= - 0.0005(x^{2}+30)(x - 20)(x - 70)=0$. The factor $x^{2}+30>0$ for all real $x$. So, we solve $(x - 20)(x - 70)=0$. Using the zero - product property, $x-20 = 0$ gives $x = 20$ and $x - 70=0$ gives $x=70$. The company's profit will be exactly $$0$ if it makes and sells $20$ or $70$ jackets.

Step2: Determine when profit is positive

From the graph of the function $y = P(x)$, the function is above the $x$-axis (positive) when $20<x<70$. The company will make a profit if it makes and sells more than $20$ but less than $70$ jackets.

Step3: Determine when profit is negative

The function is below the $x$-axis (negative) when $x<20$ or $x>70$. The company will not make a profit if it makes and sells fewer than $20$ or more than $70$ jackets.

Answer:

The company's profit will be exactly $$0$ if it makes and sells $20$ or $70$ jackets. The company will make a profit if it makes and sells more than $20$ but less than $70$ jackets, but will not make a profit if it makes and sells fewer than $20$ or more than $70$ jackets.