Question

freshflow produces organic juice bottles. the company has gathered data on revenue and expenses at different quantities. the table provides this data: quantity (q) revenue ($) expense ($) profit ($) 0 0.00 500 -500 25 2,687.5 1,000 1,687.5 50 4,750 1,500 3,250 75 6,187.5 2,000 4,187.5 100 7,000 2,500 4,500 125 7,187.5 3,000 4,187.5 150 6,750 3,500 3,250 175 5,687.5 4,000 1,687.5 based on the table, in which range of quantities do the break - even points occur where the profit is zero? between q = 0 and q = 25 between q = 25 and q = 50 between q = 50 and q = 75 between q = 75 and q = 100 between q = 100 and q = 125 between q = 125 and q = 150 between q = 150 and q = 175

Explanation:

Step1: Identify break - even points

Break - even points occur when profit is zero. We look at the profit values in the table.

Step2: Check profit values

When $q = 25$, profit is $1,687.5$ (positive) and when $q = 50$, profit is $3,250$ (positive). When $q = 75$, profit is $4,187.5$ (positive). When $q = 100$, profit is $4,500$ (positive). When $q = 125$, profit is $4,187.5$ (positive). When $q = 150$, profit is $3,250$ (positive). When $q = 175$, profit is $1,687.5$ (positive).
We note that profit changes sign between non - given values. But we can see that as quantity increases, profit first increases and then starts to decrease. By observing the trend and the fact that profit is positive for all given values, we assume that the break - even points are outside the range of positive profit values. Since profit is negative when $q = 0$ ($- 500$) and becomes positive as $q$ increases, the break - even point occurs between $q = 0$ and $q = 25$.

Answer:

between $q = 0$ and $q = 25$