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# Optimization

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There are approximately 300 customers shopping in Fackert Department Store in Mexico City between 9 a.m. and 5 p.m. on Saturdays. When deciding how many cash registers to keep open each Saturday, owner Susanna Fackert considers 2 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 \$4 per hour. When only 1 is on duty, the waiting time per customer is about 10 minutes (or 1/6 of an hour); when 2 clerks are on duty, average waiting time is 6 minutes per person; 4 minutes when 3 clerks are working; and 3 minutes with 4 clerks.

Ms. Fackert has conducted customer satisfaction surveys and has been able to estimate that the store suffers approximately \$5 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 in order to minimize the store's total expected cost.

https://brainmass.com/math/optimization/optimization-97949

#### Solution Preview

Let's look at the situation for each possible number of clerks:

One clerk:

Clerk is paid \$4/hr * 8 hrs = \$32.

Customer waiting time is 1/6 hr * 300 customers = 50 hours.

Loss of sales based on customer waiting time: 50 * \$5 = \$250

Total costs = \$32 + \$250 = \$282

Two ...

\$2.19