Question

$$ p ( x ) = - 0.0005 ( x ^ { 2 } + 30 ) ( x - 20 ) ( x - 70 ) $$ consider the graph of function p. the companys profit will be exactly $0 if it makes and sells 20 or 70 jackets, but will not make a profit if it makes and sells less than 30 jackets.

Explanation:

Step1: Analyze profit = 0

The profit \(P(x)=0\) when \(x = 20\) or \(x = 70\) (roots of the function).

Step2: Analyze profit > 0

The function \(P(x)>0\) (makes a profit) when \(20

Step3: Analyze profit < 0

The function \(P(x)<0\) (no - profit) when \(x<20\) or \(x > 70\) (from the graph, the parts of the curve below the \(x -\)axis in these intervals).

Answer:

The company makes a profit if it makes and sells between \(20\) and \(70\) jackets, but will not make a profit if it makes and sells less than \(20\) or more than \(70\) jackets.