Question

(Operations Management) The grocery store gets an average of 50 customers per shift. The manager wants to calculate whether he should hire one, two, three, or four salespeople. The average waiting times will be seven minutes with one salesperson, four minutes with two salespeople, three minutes with three salespeople, and two minutes with four salespeople. He has estimated the cost per minute that customers wait at $1. The cost per salesperson per shift (including fringe benefits) is $70. Analyze to determine how many salespeople should be hired?

Answer 1

The grocery store should hire 2 salespeople.

Please refer to the detailed explanation for calculations.

Explanation:

Total Cost per shift = Average waiting time in minutes * waiting cost per minute * number of customers per shift + Number of salespeople * cost per salesperson per shift

Waiting cost per minute = $1

Number of customers per shift = 50

Cost per salesperson per shift = $70

For 1 salesperson:

The average waiting time in minutes = 7

Total Cost per shift = 7 * 1 * 50 + 1 * 70

Total Cost per shift = $420

For 2 salespeople:

The average waiting time in minutes = 4

Total Cost per shift = 4 * 1 * 50 + 2 * 70

Total Cost per shift = $340

For 3 salespeople:

The average waiting time in minutes = 3

Total Cost per shift = 3 * 1 * 50 + 3 * 70

Total Cost per shift = $360

For 4 salespeople:

The average waiting time in minutes = 2

Total Cost per shift = 2 * 1 * 50 + 4 * 70

Total Cost per shift = $380

The Least Total Cost per shift is for the case when 2 salespeople should be hired.

Hence, the grocery store should hire 2 salespeople.