A radio manufacturer is experiencing theft problems at its warehouse and has decided to hire security guards to reduce the thefts.The firm wants to minimize the net cost of warehouse thefts. Given the above info,if each security guard is paid $200 a week and the cost of a stolen radio is $25,how many security guards should the firm hire?
A)1
B)2
C)3
D)4

Question

A radio manufacturer is experiencing theft problems at its warehouse and has decided to hire security guards to reduce the thefts.The firm wants to minimize the net cost of warehouse thefts.  Given the above info,if each security guard is paid $200 a week and the cost of a stolen radio is $25,how many security guards should the firm hire?
A)1 
B)2 
C)3 
D)4

Quizplus · Accepted Answer

The firm wants to minimize the net cost of warehouse thefts, which means they want to minimize the cost of thefts minus the cost of hiring security guards. Let's assume x is the number of security guards the firm hires. The cost of thefts without security guards would be $25 for each stolen radio. With security guards, the cost of thefts is the probability of a theft happening (p) multiplied by the cost of a stolen radio ($25) multiplied by the number of thefts per week (which we do not have information about). The cost of security guards is $200 per security guard per week, so the net cost would be:

Net Cost = Cost of thefts - Cost of security guards
Net Cost = 25p - 200x

The firm wants to minimize the net cost, so they need to find the minimum point of this function. To do this, they need to take the derivative of the function and set it equal to zero:

d/dx (25p - 200x) = -200
-200 = 0

This means that the net cost reaches its minimum point when x = 0. However, this is not a valid solution because the firm needs to hire at least one security guard to reduce thefts. Therefore, they should hire at least one security guard, which would cost the firm $200 per week. They could also hire two security guards for $400 per week, which would further reduce the probability of thefts and potentially save the firm money in the long run. However, hiring three or more security guards would not result in a significant reduction in thefts and would not be cost-effective. Therefore, the best choice is:

B) 2

A Radio Manufacturer Is Experiencing Theft Problems at Its Warehouse