Question

The function ​R(x)equals108 StartRoot x EndRoot gives the total revenue per year in thousands of dollars generated by a small business having x employees. Use this function to evaluate ​R(12​)minus​R(11​). If the salary for the twelfth employee is $ 26 comma 000​, is it a good decision to hire the twelfth ​employee?

Answer 1

Explanation:

We are given that
`R(x) = 108\sqrt[]{x}` is the revenue for having x employees.

Let us calculate the following

`R(12)-R(11) = 108\sqrt[]{12}-108\sqrt[]{11} = 15.93` REcall that is amount represents the revenue that having one extra employee would have.

We have that the salary of the 12th employee would be 26000. One criteria to define if it's a good idea to hire the 12th employee is to check if the profit for having an extra employee is positive. We will take the revenue of the extra employee minus the cost and check if it is positiv. Then,

`(108\sqrt[]{12}-108\sqrt[]{11})\text{(revenue for 12 employees)}-26000\text{(cost for the 12th employee} =-25984<0`

Since it is a negative amount, this means that it would be more expensive to have one extra employee than the revenue it would generate. Therefore, it won't be suitable to hire the 12th employee