agency is having problems with personal phone calls made during working hours.Each minute of a personal call costs the agency $0.50 in wasted wages.The agency hires operators to monitor calls in order to attain the optimal number of personal calls minimize total cost of personal calls). Based on the above information,if operators receive $25 an hour,how many operators should the agency hire?
A)0
B)1
C)2
D)3

Question

agency is having problems with personal phone calls made during working hours.Each minute of a personal call costs the agency $0.50 in wasted wages.The agency hires operators to monitor calls in order to attain the optimal number of personal calls minimize total cost of personal calls).  Based on the above information,if operators receive $25 an hour,how many operators should the agency hire?
A)0 
B)1 
C)2 
D)3

Quizplus · Accepted Answer

Let's assume that the agency wants to hire x operators to monitor personal calls.

The cost of one operator per hour is $25. Therefore, the total cost of x operators per hour would be $25x.

Now, let's find out the cost of personal calls made by employees during working hours.

According to the problem, each minute of a personal call costs $0.50 in wasted wages.

Let's assume that the total time spent on personal calls per hour by all the employees is t minutes.

Therefore, the cost of personal calls per hour would be 0.5t.

The agency wants to minimize the total cost of personal calls.

So, the total cost would be the sum of the cost of operators and the cost of personal calls.

Total cost = $25x + 0.5t

Now, the problem is to find out the optimal number of operators (x) to minimize the total cost of personal calls.

To do that, we need to differentiate the total cost with respect to x and equate it to zero.

d(Total cost)/dx = 25

Therefore, x = 0.02t

This means that the optimal number of operators to minimize the total cost of personal calls is 0.02 times the total time spent on personal calls per hour.

For example, if the employees spend 100 minutes on personal calls per hour, then the optimal number of operators would be:

x = 0.02t = 0.02(100) = 2

So, the agency should hire 2 operators to monitor personal calls during working hours to minimize the total cost of personal calls.

Therefore, the answer is (C) 2.

Agency Is Having Problems with Personal Phone Calls Made During