Unit 8 Exercise

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Yorkville University *

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Feb 20, 2024

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WWW.YORKVILLEU.CA Unit 8 Exercise - Part 1 Yorkville University BUSI2113-23F-O-D Jeremy Seymour NOV 30, 2023

WWW.YORKVILLEU.CA 8.1 students arrive at the help desk at the rate of 4 every 10 minutes. The average service time is 2 minutes The Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed. 0.4 average time a student is in the lab 0.5 =1/(0.5- 0.4 ) 10 mins average number of students in the lab 0. 4/(0.5-0.4) 4 average number of students waiting to receive service 0.4^2/0.5*(0.5-0.4) 3.2 average time a student is in the queue 0. 4/0.5*(0.5-0.4) 0.08 mins What is the probability that there are no students at the computer lab 1-0.4/0.5 20% What percentage of the time is the help desk busy 0.4/0.5 80% What is the probability that there are exactly 2 students in the lab? p2 e 0.6703 5% ((e0.4*(0.4^2))/2) By how much would your answer to part (a) be reduced if a second help desk, which could do the same work, were added p0= m=2 1/ 1+0.4/0.5 1/2*(0.4/0.5)^2 x (0.4*0.5)/((0.4*0.5)-2) 1.8 0.32 -0.11111111 = 0.56675063 ls 0.128 =0.4*0.5*(0.4/0.5)^2 0.36 =1*(1-0.4)^2 +0.36/0.57 0.201511 0.128/0.36 0.355555556 + 0.4/0.5 0.8 = 1.001511 ls ws 2.5037783 2.5 mins ls/0.4 reduced by 7.5 mins 10 mins -2.5mins avg num of arrival /min avg num served/min

WWW.YORKVILLEU.CA 8.2 5 weaving machines in use need repair after about 20 hours of use the maintenance worker can service a weaving machine in an average of 2 hours Weaving machine downtime costs $120 per hour. Jim is paid $25 per hour aver arr rate /hr 0.25 5/20 avg ser rate/hr c) What is the total hourly costs? 0.5 1/2 n 5 a) What is the average time a weaving machine is waiting to be repaired? 1 hr b) What is the average number of weaving machines in the repairing area? lq 0.25 ls 0.75 per hr c) What is the total hourly costs? 145 per repair average time a weaving machine is waiting to be repaired*(Weaving machine downtime costs $120 per hour +Jim is paid $25 per hour) =+aver arr rate/((2*avg ser rate)*(avg ser rate-aver arr rate)) =+aver arr rate^2/((2*avg ser rate)*(avg ser rate-aver arr rate)) lq+aver arr rate /avg ser rate

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WWW.YORKVILLEU.CA 8.3 William consider price and reputation as the most important criteria He considers reputation to be four times more important than price choices to two suppliers On a 10-point scale, he has assigned Rideau’s Windows Supply a score of 9 on price and 4 on reputation. He has assigned Ian and Family a score of 3 on price and 6 on reputation. Rideau’s Windows Supply crtterion weight score(1-10) weight X score reputation 0.8 4 3.2 price 0.2 9 1.8 tatal 1 13 5 Ian and Family reputation 0.8 6 4.8 price 0.2 3 0.6 tatal 1 9 5.4

WWW.YORKVILLEU.CA 8.4 its engines valued at $500,000 The engines need to be shipped to the Montreal, QC, plant The annual holding cost rate for auto engine has been estimated at 15%. There are five shipping companies available Their delivery time and costs are listed in the table below. Which carrier is most economical? time(days) cost shipping day saved Daily holding cost saved money saved a 20 500 0 0 0 b 15 800 5 1027.39726 227.3972603 c 12 1200 8 1643.835616 443.8356164 d 8 1600 12 2465.753425 865.7534247 e 5 2000 15 3082.191781 1082.191781 Carrier x-carrier a Daily holding cost Daily holding cost SAVED (longest) DAYS X DAYS SAVED - COST annual holding cost rate 15% product value 500,000 (annual holding cost rate x product value) /365 Daily holding cost 205.4794521 : Carrier e saved the most money

Unit 8 Exercise

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