The manager of the customer service department at a bank can hire employees with a high school degree HS)who earn $10,000 annually or employees with a bachelor's degree B)who earn $20,000.The manager wants to maximize the number of customers served given a fixed payroll. Given the above info,if the manager has a payroll of $80,000,how should the budget be allocated in order to maximize the number of customers served?
A)Hire two HS and three B.
B)Hire four HS and two B.
C)Hire one HS and two B.
D)Hire three HS and one B.

Question

The manager of the customer service department at a bank can hire employees with a high school degree HS)who earn $10,000 annually or employees with a bachelor's degree B)who earn $20,000.The manager wants to maximize the number of customers served given a fixed payroll.  Given the above info,if the manager has a payroll of $80,000,how should the budget be allocated in order to maximize the number of customers served?
A)Hire two HS and three B. 
B)Hire four HS and two B. 
C)Hire one HS and two B. 
D)Hire three HS and one B.

Quizplus · Accepted Answer

Let x be the number of HS employees and y be the number of B employees. The objective is to maximize the number of customers served, which is proportional to the total number of employees, i.e. maximize x+y subject to the payroll constraint of $80,000. Mathematically, this can be represented as:

10,000x + 20,000y ≤ 80,000
x + y ≤ 8

To maximize x+y, we need to allocate the payroll equally between HS and B employees, i.e. spend $40,000 on each type. Since HS employees cost half as much as B employees, we can hire twice as many HS employees as B employees, i.e. x = 2y. Substituting this into the payroll constraint, we get:

10,000(2y) + 20,000y ≤ 80,000
y ≤ 2

Since y has to be an integer, the only feasible value is y = 2, which gives x = 4. Therefore, the optimal allocation is to hire four HS employees and two B employees.

The Manager of the Customer Service Department at a Bank