Mr. Cheney owns a large gas station in Vermont. The average and standard deviati

Question

Mr. Cheney owns a large gas station in Vermont. The average and standard deviation of inter-arrival times of cars stopping by for re-fueling is 3 minutes. If all the pumping stations are full, cars will bypass Mr. Cheney’s gas station for one further up the road (which also happens to charge the same price). Currently, Mr. Cheney has 6 pumping stations and on the average, it takes 5 minutes to service a vehicle which has stopped by for refueling. You are required to answer the following questions: a) What percentage of the time will a customer bypass Mr. Cheney’s gas station. b) What is the average number of customers served per hour. c) Assume that it costs Mr. Cheney $ 12.50 in lost profit per customer lost. It is possible to add 3 more pumping stations at an amortized cost of $ 1.50 per hour. Should Mr. Cheney add the additional 3 pumping stations?

Explanation / Answer

average time of arrival is 3 min

total service time = 5 min

prob that a car will pass 1 pumping station = (5-3)/3 = 0.66

percentage of the time will a customer bypass (all 6 pumping station) = 0.666 *100=8.26 %

b)

Average no of custumer arriving per hour = 60/3= 20

% passing= 8.26 %

% served = (100-8.26)*20/100 = 18.35 customers not served = 20-18.35=1.65 person/hr

c)

after addind 3 more pumping station chance to bypass= 0.669 =2.38 % =2.38/100*20 = 0.476 person /hr

total benifit =12.5(1.65-.476) =$14.675

total cost = 3*1.5= $4.5

profit> cost

hence Cheney can add 3 more pumping stations

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