Trucks arrive at the loading dock of a wholesale grocer at the rate of 1.2 per h
ID: 414913 • Letter: T
Question
Trucks arrive at the loading dock of a wholesale grocer at the rate of 1.2 per hour. A single crew consisting of two workers can load a truck in about 30 minutes. Crew members receive $10 per hour in wages and fringe benefits, and trucks and drivers reflect an hourly cost of $69. The manager is thinking of adding another member to the crew. The service rate would then be 2.4 trucks per hour. Assume rates are Poisson.
A) Would the third crew member be economical? (Round your intermediate and final answer to 2 decimal places. Omit the "$" sign in your response.)
Yes because the total cost is $?
B) Would a fourth member be justifiable if the resulting service capacity were 2.6 trucks per hour? (Round your intermediate and final answer to 2 decimal places. Omit the "$" sign in your response.)
No because the cost would be $?
B) Would a fourth member be justifiable if the resulting service capacity were 2.6 trucks per hour? (Round your intermediate and final answer to 2 decimal places. Omit the "$" sign in your response.)
Explanation / Answer
service rate = 2 trucks per hour
a)
Average number of trucks in system
Ls = Lq + r
= lambda^2/u(u-lambda) + lambda/u
= 1.2^2/2(2-1.2) + 1.2/2
= 0.9 + 0.6
= 1.5 trucks
total cost of 2 members = 2* 10 + 1.5 * 69
= 20 + 103.5
= 123.5 per hour
with 3 crew memebers
average number of trucks = (1.2)^2/2.4*(2.4-1.2) + 1.2/2.4
= 0.5 + 0.5
= 1 truck
total cost = 3*10 + 1*69
= 99 per hour
hence cost for company decreases after employing third crew member hence its economical
b)
average number of trucks in system
= (1.2)^2/2.6*(2.6-1.2) + 1.2/2.6
= 0.4 + 0.5
= 0.9 truck
total cost = wages of crew members + cost of truck
= 4 * 10 + 0.9 * 69
= 102.1
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