To find: The value of and the reason that why the company wants to hire more workers if .
The value of is .
The average productivity of the workforce at the plant is shown below with an equation.
Calculate the value of .
Differentiate equation (1) with respect to .
Apply the quotient rule below.
Substitute for and for in the above equation.
If the condition is true, then is increasing. For the condition to be true, the total value of production in the plant should increase. It shows that the average productivity will increase, as the size of the workforce increases. The company will be interested in hiring more workers.
To show: The condition is true, if the expression is greater than the average productivity.
For the given condition, is greater than the average productivity, that is,
Substitute for in the equation (2).
Multiply by on both sides of the above equation.
Here, the condition is true.
Thus, is increasing that means that the average productivity will increase as the size of the work force increases.
Hence the condition is verified, if the value of is greater than the average productivity.
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