Eric owns a small car wash business. He follows a fairly simple process to wash

Question

Eric owns a small car wash business. He follows a fairly simple process to wash the cars. Answer the following question about his process. Assume that the capacity of his equipment is 4 cars at a time and that he starts with a single worker.

A. If customers arrive every 8 minutes, and there is only 1 car per customer order, how many cars can Eric finish (sell) per 6-hour shift? Eric circle time is 8 minutes and the equipment time 16 minutes

A. How long does the entire system take to complete one car

B. What is the utilization of a single worker (Eric) be? What will the utilization of the equipment be?

C. If each car is done for $15 and the cost of input (chemicals) is $5, what amount of profit (excluding the cost of labor) can Eric make per hour?

What would the value of a second be? What would be the utilization of the workers be if a second worker is hired?

D. Evaluate the value of a reduction in the price of a car wash to $10 if that would result in an average of 1 customer every 6 minutes. Assume that there are 2 workers at the end of part C.

Explanation / Answer

1) as the equipment time is 16 min the whole process will take 16 min to complete the car wash.

2) utilization of eric =1/8 =12.5%

utilization of equipment= 4/16=25% because 4 cars can be washed at a time with the equipment.

3) customer arrival rate= 1per 8 min

equipment circle time=16 min

2 cars can be washed every 16 min

but there is only 1 worker so only 1 car can be washed in 16 min

so in 1 hour or 60 min = 3.75

there cannot be 3.75 customers thus 3customers

profit per car=$15=$5=$10

profit for 7 cars= 3*$10=$30

if a second worker is hired 2 cars can be washed simultaneously in the equipment

but customer arrival rate =1per 8 min so profit would be =$70

utilization of workers = 2/8=25%

d) customer arrival rate=1/6

equipment circle time = 1/16

so in every 6 min 2.6 cars can be washed

but 2.6 cars cannot be washed therefore, 2 cars can be washed every 16 min.

and there are 2 workers

so the profit made every 16 min =$10-$5=$5

profit made in 1 hour= $18.75

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