Question

You are the manager of a clothing store. You must decide how many of your employees to put on the sales floor, and how many to put on the register. Because employees on the sales floor cause customers to buy more products, if you do not have at least 2 employees on the register for every 5 employees working on the sales floor, your registers will get very clogged and you will lose business. You have a total of 84 employees, and you wish to have as many on the sales floor as possible. How should you divide your employees?
a.
44 on the sales floor, 40 on the register
b.
55 on the sales floor, 29 on the register
c.
60 on the sales floor, 24 on the register
d.
75 on the sales floor, 9 on the register

Answer 1

Let S = employees on the sales floor and R = employees on the register. You need R ≥ (2/5)S and S + R = 84, so

84 − S ≥ (2/5)S ⇒ 84 ≥ (7/5)S ⇒ S ≤ (5/7)·84 = 60.

So the maximum possible on the sales floor is 60, with 24 on the register. Answer: c.