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Math problem set 6

Math problem set 6

Part 1 of 2 – Part 1

This part of the question is based on the following information.

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.

Please fill out the following table to answer the quiz questions in Part 1. (You may also download the attached worksheet.)

                                                           Number of checkout clerks                        
                                                              1               2           3             4
Number of customers                         300            300     300            300
Average waiting time (per customer)  
Total customer waiting time
Cost per waiting hour
Total waiting cost
Checkout clerk hourly salary
Total pay of clerks for an 8-hour shift
Total expected cost                                

 
Question 1 of 10
10.0 Points
The total customer waiting time is What’s This?
Question 2 of 10
10.0 Points
The total wait cost is What’s This?
Question 3 of 10
10.0 Points
The total cost of hiring is only What’s This?
Question 4 of 10
10.0 Points
To minimize the total expected cost based on your calculations above, the optimal number of clerks to have on duty each Sunday is ___________.

 
 
 
 

Reset Selection

What’s This?

Part 2 of 2 – Part 2

This part of the question is based on the following information.

The wheat harvesting season in the American Midwest is short, and most farmers deliver their truckloads of wheat to a giant central storage bin within a two-week span. Because of this, wheat-filled trucks waiting to unload and return to the fields have been known to back up for a block at the receiving bin. The central bin is owned cooperatively, and it is to every farmer’s benefit to make the unloading/storage process as efficient as possible. The cost of grain deterioration caused by unloading delays, the cost of truck rental, and idle driver time are significant concerns to the cooperative members. Although farmers have difficulty quantifying crop damage, it is easy to assign a waiting and unloading cost for truck and driver of $18 per hour. The storage bin is open and operated 16 hours per day, 7 days per week, during the harvest season and is capable of unloading 35 trucks per hour according to an exponential distribution. Full trucks arrive all day long (during the hours the bin is open) at a rate of about 30 per hour, following a Poisson pattern.

The cooperative, as mentioned, uses the storage bin only two weeks per year. Farmers estimate that enlarging the bin would cut unloading costs by 50% next year. It will cost $9,000 to do so during the off season.

 
Question 5 of 10
10.0 Points
The average number of trucks in the system is What’s This?
Question 6 of 10
10.0 Points
The average time per truck spent in the system is What’s This?
Question 7 of 10
10.0 Points
The utilization rate for the bin area is What’s This?
Question 8 of 10
10.0 Points
The probability that there are more than 3 trucks in the system is about What’s This?
Question 9 of 10
10.0 Points
The total daily cost in the unloading process is What’s This?
Question 10 of 10
10.0 Points
Based on the above calculation, the net saving/loss of enlarging the bin is What’s This?

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