our Wheel Tire $hop is a single bay tire store located in

Ames, Iowa. The interarrival time of cars in need of tires

follows a uniform distribution with times between $10$ and

$50$ minutes. Twenty percent of arriving customers want a

single tire replaced, $40\%$ want two tires replaced, $5\%$

want three tires replaced, and $35\%$ want all four tires replaced. Customer service time approximately follows a

uniform distribution that varies with the number of tires

that need to be replaced. The following statistics hold:

N u m b er o f T ires S er v ice T im e Is U n iform ly

N eed in g R ep la cem en t D istrib u ted B etw een

$110$ minutes and $20$ minutes

$215$ minutes and $35$ minutes

$320$ minutes and $40$ minutes

$425$ minutes and $50$ minutes

The owner of the store, Ben $tern, is considering leasing a

new computerized tire balancing machine, which will reduce the average service time, resulting in the following

uniform service distributions:

N u m b er o f T ires S er v ice T im e Is U n iform ly

N eed in g R ep la cem en t D istrib u ted B etw een

$18$ minutes and $18$ minutes

$212$ minutes and $32$ minutes

$315$ minutes and $35$ minutes

$420$ minutes and $40$ minutes

The machine lease cost averages $$1\mathrm{.}50$ per hour. Mr$.$

Stern estimates that the goodwill cost of a customer$$s

being in the tire shop $($either being served or waiting to be

served$)$ is $$4\mathrm{.}00.$

Use Excel to perform the simulation analysis and prepare a business report for Mr$.$ $tern recommending

whether or not he should lease the machine. Include in

your report relevant service statistics, such as the average

time a customer spends waiting to begin service as well

as time in the system using both the existing tire balancing machine and the proposed computerized balancing

machine. Each simulation run should cover at least $1000$

cars.