# Counting Grocery Lanes

The Schmedley Discount Department Store has approximately 300 customers shopping in its store between

9 A.M. and 5 P.M. on Saturdays. In deciding how many cash registers to keep open each Saturday,

Schmedley's manager considers two factors:customer waiting time (and the associated waiting

cost) and the service costs of employing additional checkout clerks. Checkout clerks are paid an average

of $8 per hour. When only one is on duty, the waiting time per customer is about 10 minutes (or

hour); when two clerks are on duty, the average checkout time is 6 minutes per person; 4 minutes

when three clerks are working; and 3 minutes when four clerks are on duty. Schmedley's management has conducted customer satisfaction surveys and has been able to estimate that the store suffers approximately $10 in lost sales and goodwill for every hour of customer time spent waiting in checkout lines. Using the information

provided, determine the optimal number of clerks to have on duty each Saturday to minimize the

store's total expected cost.

https://brainmass.com/math/synthetic-geometry/counting-grocery-lanes-464024

#### Solution Preview

I've attached my answer in the word document.

1 clerk 2 clerks 3 clerks 4 clerks

Service cost

Per day 1 clearkx

$8 per clerk hourx

8 hours per day=

$64 per day 2 clerksx

$8 per clerk hourx

8 hours per day=

$128 per day 3 clerkx

$8 per clerk hourx

8 hours per ...

#### Solution Summary

The solution assists in counting grocery lanes.