Homework #11 Solutions
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School
Texas A&M University *
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Course
301
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
7
Uploaded by EarlEmu298
AGSM 301 Homework #11 Solutions 1.) (20 point) a. 2 pts b.
4 pts c.
2 pts d-k. 1 pt.
a.) Piles Trucks b.) State 00: 1 FEL idle State 10: 2 FEL idle State 01: 1 FEL idle State 11: 1 FEL idle c.) FEL loading trucks in states 01 and 11. d.) Truck being loaded from lot in state 01. e.) Truck being loaded from pile in state 11. f.) There is never an idle truck. Trucks are only present in states 01 and 11, and in both cases, they are being loaded. g.) FEL making a pile in state 00. h.) i.)
What is the arrival rate (tons per hour)? a.
30 tons/hr. j.)
What is the service rate from the pile (tons per hour)? b.
20 tons/hr. k.)
What is the service rate from the field (tons per hour)? c.
10 tons/hr. 2. (20 point) 0 0 0 1 1 0 1 1 μ2 is greater than μ1 because the FEL doesn't have to go scoop manure from the lot, but it loads directly from a premade pile. This saves time.
Excel sheet work 5 pts l.
4 pts m-p 1 pt. or 2 pts for m-p and 4 pts for l m.
What is the average service rate (tons per hour) of removing manure from the lot? P01(u1)= 0.621(10)=6.21 tons/hr. n.
What is the average service rate (tons per hour) of removing manure from the pile? P11(u2) = 0.103(20) = 2.06 tons/hr. o.
What is the average service rate (tons per hour) of the entire model? P01 (u1) + P11 (u2) = 6.21 + 2.06 = 8.27 tons/hr. p.
How many 10-hour days is required to remove 750 tons? 750
tons/8.27 tons/hr. = 90.68 hrs. = 9.07 10-hr days 3. (10 point) l. What are the values for P00, P01, P10, and P11? P00=0.21 P01=0.62 P10=.07 P11=.10
6 pts for a 2 pts for b λ= 40 products/
hr. c = 3 4. (15 point) μ= 1 5 products/hr. = 0.0 28 = 227.6 *0.0 28 + 2.7 = 9.04 = 6.37 = 0.1 6 hr.= 9.6 min a. W = L/lambda = hr. = 13.6 min 0.23 b. Yes, if WQ no if W
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5 pts for a, b and c
λ= 45 products/
hr. 5. (15 points) a.
3 pts b.
2 pt. c.
2 pts d.
4 pts e.
4 pts
a. One truck is being loaded by the pile, one truck is being loaded from the field and another truck is idle. One FEL is loading a truck from a pile and the other FEL is loading a truck from the field. b. One truck is in the queue c.
12 and 13 d.
truck μ=30 products/hr. c=2 a. = 0.143 b. = 13.5*0.07+1.5 = 2.45 = 0.945 c. = 0.021 hr.=1.26 min
00 0 01 0 02 1 03 1 10 0 11 0 12 1 13 1 e.
FEL 00 0 01 0 02 0 03 0 10 2 11 1 12 1 13 0 6. (20 point)
5 pts for excel a)
What is the rate of removal (tons per hour) of manure from the field? (2 pts)
μ1(P01+P02+2*P03+P11+P13) + μ2(P12+P13) = 73.58 tons/hr. b)
How many 10-hour days will it take to remove 750 tons of manure from the site? (2 pts)
73.58 tons/hr. * 10 hrs. = 735.8 tons/day 750tons / (735.8 tons/day) = 1.02 days c)
Based on the percent of time that 1 or more trucks are idle, for how many hours are trucks idle during the week? (2 pts)
10*(P02+P03 + P12+P13) = 2.88 hrs. d)
Based on the percent of time that 1 or more front-end loaders are idle, for how many hours are front-end loaders idle during the week? (2 pts)
10
(2*P10+P11+P12) = 9.10 hrs. e) What is the average percent of time that trucks are idle?
(2 pts)
100*((P02+P03 + P12+P13)/3) = 9.6% hrs./truck f)
What is the average percent of time that front-end loaders are idle? (1 pts)
100 * ((2*P10+P11+P12)/2) = 45.5% hrs./truck
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g)
How many 10-hour days does it take if only loaded from the field? (2 pts)
(μ1(P01+P02+2*P03+P11+P13)) * 10 = 463.38 tons/day 750 tons/ 463.38 tons/day = 1.62 days h)
How many 10-hour days does it take if only loaded from the pile? (1 pts)
(μ2(P12+P13
)) *10 = 272.51 tons/day 750 tons / 272.51 tons/day = 2.75 days i)
What would your recommendation be to the manager of the operation to move the tons of manure most efficiently? (1 pts)
Opinion based