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 budget constraint is:
10,000x + 20,000y ≤ 80,000
Simplifying, we get:
x + 2y ≤ 8
We want to maximize the number of customers served, which we can assume is proportional to the number of employees hired. Therefore, we want to maximize x + y subject to the budget constraint.
One way to do this is to graph the feasible region (the shaded area in the picture):
https://i.imgur.com/1dVii1A.png
The feasible region is the area below the line x + 2y = 8 and to the right of the x and y axes. The corners of the feasible region are (0,0), (0,4), (2,3), and (4,2).
Evaluating x + y at each corner, we get:
(0,0): 0
(0,4): 4
(2,3): 5
(4,2): 6
Therefore, the maximum value of x + y is 6, which occurs when we hire 4 HS employees and 2 B employees.

The Manager of the Customer Service Department at a Bank