Question

Sandra has analyzed the projections of her new business. She has determined that the function f(x) = (x)/(x + 4) will represent her total expenses and the function g(x) = (x + 3)/(2x + 3) will represent her total revenue, where x is the number of units sold, in thousands. How many units, in thousands, must Sandra sell to keep her total revenue above her total expenses?

A) 3.
B) 6.
C) 12.
D) 18.

Answer 1

Sandra must sell more than 6,000 units to keep her total revenue above her total expenses, which corresponds to option B) 6.

Step-by-step explanation:

To determine the number of units Sandra must sell to keep her total revenue above her total expenses, we need to find when g(x) > f(x). This means we want to solve the inequality (x + 3)/(2x + 3) > x/(x + 4). To find the solution, we can cross-multiply and simplify the resulting inequality. By doing so, we derive that Sandra must sell more than 1,000 units to ensure her revenue exceeds her expenses. We then check the answer options to identify the smallest number of thousands of units that is still greater than 1,000 units, which gives us the answer.

After resolving the inequality, we find that the answer is option B) 6, meaning Sandra must sell more than 6,000 units (in thousands) to keep her revenue above her expenses.