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A new strip mall is being considered and the developers want to determine how many parking spaces there should be. It is assumed that if the lot is full, an arriving car will leave. Cars arrive at a rate of 15/hour. The average time a customer spends shopping is 30 minutes. Assume the interarrival times and the shopping times are exponentially distributed. Assume the average shopper purchases $150 worth of merchandise and also assume the mall is open 12 hours/day, 350 days/year.
a) If there are 10 spaces, determine the throughput rate of cars departing after completing shopping, the expected number of cars in the parking lot and the rate of lost revenue due to cars leaving because they could not find a space to park.
b) Assume the cost to create a parking spot is $2500. Assuming a 5 year horizon and an internal interest rate of 15%, how many spots should be built to minimize the combined construction and lost revenue costs?

Respuesta :

Answer:

The responses to the given question can be defined as follows:

Explanation:

For point a:

Car arrival time[tex]= \frac{15}{hour}[/tex]

Each car arrives at an interval of time of [tex]\frac{60}{15} = 4\ minutes[/tex]

process time [tex]=0.5 \ hour[/tex]

The number of vehicles moving in an hour equals 2 per hour.

As [tex]\frac{15}{2}[/tex] is greater than 1. The device will not work, resulting in such a revenue loss.

Within 44 minutes, a parking lot would be completely full, with only 1 person being serviced, and then the next empty slot would be completed 64 minutes later.

The system's production capacity is 8.5 per hour [a person entering at 0 will exit at 30]. The person that comes in at 4 will leave at 34. Roughly 50 customers would be supported for an hour.

For point b:

The number of customers would be [tex]= 8.5 \times 12 = 102[/tex] for a 12-hour time frame.

Total cost=[tex]12\times 150 = \$1800[/tex]

The total number of customers to be served at an expense of [tex]2500= \frac{2500}{150} = 18[/tex] customers.

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