Need Help with math question

[Goo_wak_jai]

For all you smart beyond members please help!!!

EZSkut rents out power scooters at a large shopping complex. They currently employ one repair person who works 8 hours/day performing emergency repairs for their fleet of 100+ scooters (or waiting for a scooter that needs repair when there aren’t any). On average, 6.5 scooters per day arrive in the shop requiring emergency repair. It takes the repair person an average of 0.6 hours to perform emergency repair on a scooter (assume negative exponential distribution). Assume that the time spent for a scooter being repaired or waiting for repair costs $20 per hour in lost revenue (the scooters are rented out during the same 8 hours/day that the mechanic works). What would be the difference in total cost (in wages plus lost revenue per day) if a second repair person were hired at $10/hour? (Assume that they would work at the same rate as the first repair person, and would work 8 hours/day fixing or waiting to fix scooters.)

[Goo_wak_jai]

Please post how you got the question. Thanx

[scat19]

I think the question is vague.

Do all 6.5 scooters come in at the start of the morning? Meaning some are waiting = more money lost per day?

Or do they come in staggered?. I got 2 completely different answers.

[CUG]

Originally posted by Goo_wak_jai
For all you smart beyond members please help!!!

EZSkut rents out power scooters at a large shopping complex. They currently employ one repair person who works 8 hours/day performing emergency repairs for their fleet of 100+ scooters (or waiting for a scooter that needs repair when there aren’t any). On average, 6.5 scooters per day arrive in the shop requiring emergency repair. It takes the repair person an average of 0.6 hours to perform emergency repair on a scooter (assume negative exponential distribution). Assume that the time spent for a scooter being repaired or waiting for repair costs $20 per hour in lost revenue (the scooters are rented out during the same 8 hours/day that the mechanic works). What would be the difference in total cost (in wages plus lost revenue per day) if a second repair person were hired at $10/hour? (Assume that they would work at the same rate as the first repair person, and would work 8 hours/day fixing or waiting to fix scooters.)

They currently employ one repair person who works 8 hours/day performing emergency repairs for their fleet of 100+ scooters (or waiting for a scooter that needs repair when there aren’t any).

-$80

On average, 6.5 scooters per day arrive in the shop requiring emergency repair. It takes the repair person an average of 0.6 hours to perform emergency repair on a scooter (assume negative exponential distribution).

-36 Minutes per repair, total of 234 minutes of repair work, or 3.9 hours

Assume that the time spent for a scooter being repaired or waiting for repair costs $20 per hour in lost revenue (the scooters are rented out during the same 8 hours/day that the mechanic works).

-$130 for the "6.5" Scooters being worked on per day in lost revenue. Plus $80 for the tech @ $10 an hour, $210 total loss here per day. The lost revenue is in the rental fees, as opposed to the cost of the technician I'm assuming, since he's a fixed cost.

What would be the difference in total cost (in wages plus lost revenue per day) if a second repair person were hired at $10/hour? (Assume that they would work at the same rate as the first repair person, and would work 8 hours/day fixing or waiting to fix scooters.)

-The addition of another Tech is $80 per day. We're trying to reduce the $20/hour lost revenue. These scooters are getting out the door quicker, a 3.9 hour workload divides in half to each tech to 1.95 which makes 3.25 of the scooters available in half the time. Daily, this only brings out $65 in increased revenue while the tech costs $80.

To me, this is not economical if you're only seeing 6.5 scooters in downtime during an 8 hour day.

Labour is fixed at $80 per tech/$160
Lost revenue at $130
Total loss $290

I believe you would lose an additional $15 per day with the hiring of another technician.
I'm not very good at math, but that's how it adds up for me.

[CUG]

Can someone check my math on that?

[nonlinear]

i can't believe you're doing this kid's homework for him :facepalm:

EDIT: plus, you're using the average repair time but i think you're supposed to assume a neg exponential distribution.

[CUG]

Originally posted by nonlinear
i can't believe you're doing this kid's homework for him :facepalm:

EDIT: plus, you're using the average repair time but i think you're supposed to assume a neg exponential distribution. Using what data though? If this scooter company will give me access to its books from the last 2 years, I could make the assertion.

I don't see anything indicating deviation from having scooters pumped out 8 hours per day at $20 an hour.

I don't know if the mechanic is a newfie alcoholic who's going to call in drunk 7 days out of the month, and I'm not sure if the new employee isn't a millenial who feels entitled to half of my profits just for walking in the door.

The best case scenario in this situation is that none of the scooters fail, and are all rented at the same time for 8 hours of the day. 100 scooters, at $20/hour $2000 an hour for 8 hours so $16,000 per day in revenue and 160 per day in costs for the employees.

[scat19]

That is what I got Cug, however, your second numbers are not right. If the scooters are coming out faster, your lost revenue is cut in half, because they are being repaired twice as fast.

130 -> 65.

65+ 160 =225

I agree, one repair person is adequate.

IRL - 15 dollars extra per day is worth it if customer satisfaction is higher = more positive reviews = more units for rent = more customers.

Also - the second employee cost is higher with benifits (if any), higher insurance costs, etc. This question is really flawed IMO haha.

[The_Rural_Juror]

Originally posted by Goo_wak_jai
Please post how you got the question. Thanx

I got the question from here (http://forums.beyond.ca/showthread.php?s=&postid=3158770#post3158770)

[scat19]

Originally posted by The_Rural_Juror


I got the question from here (http://forums.beyond.ca/showthread.php?s=&postid=3158770#post3158770)
:rofl: :devil:

[psycoticclown]

You guys can't just do this by regular methods, its a waiting lines/queuing problem.

This shits easy, plug into POM/QM. Lamda is 0.8125, mu is 1.666667

Resuts for one mechanic only:
Average Server Utilization: 0.49
Average number in the queue(Lq): 0.46
Average number in the system(Ls): 0.95
Average time in the queue(Wq): 0.57 34.24min 2054.21s
Average time in the system(Ws): 1.17 70.24min 4214.47
Cost (Labor + # waiting*wait cost): $19.27
Cost (Labor + # in system*wait cost): $29.02

Results for 2 Mechanics:
Average Server Utilization: 0.24
Average number in the queue(Lq): 0.03
Average number in the system(Ls): 0.52
Average time in the queue(Wq): 0.04 2.27min 136.44s
Average time in the system(Ws): 0.64 38.27min 2296.44s
Cost (Labor + # waiting*wait cost): $20.62
Cost (Labor + # in system*wait cost): $30.37

Total difference in cost is a loss of $1.35 per hour if you get a second mechanic.

[CUG]

Originally posted by psycoticclown
You guys can't just do this by regular methods, its a waiting lines/queuing problem.

This shits easy, plug into POM/QM. Lamda is 0.8125, mu is 1.666667

Resuts for one mechanic only:
Average Server Utilization: 0.49
Average number in the queue(Lq): 0.46
Average number in the system(Ls): 0.95
Average time in the queue(Wq): 0.57 34.24min 2054.21s
Average time in the system(Ws): 1.17 70.24min 4214.47
Cost (Labor + # waiting*wait cost): $19.27
Cost (Labor + # in system*wait cost): $29.02

Results for 2 Mechanics:
Average Server Utilization: 0.24
Average number in the queue(Lq): 0.03
Average number in the system(Ls): 0.52
Average time in the queue(Wq): 0.04 2.27min 136.44s
Average time in the system(Ws): 0.64 38.27min 2296.44s
Cost (Labor + # waiting*wait cost): $20.62
Cost (Labor + # in system*wait cost): $30.37

Total difference in cost is a loss of $1.35 per hour if you get a second mechanic. :rofl: or $10.80 per day. I was out by $4.20

[Goo_wak_jai]

Originally posted by psycoticclown
You guys can't just do this by regular methods, its a waiting lines/queuing problem.

This shits easy, plug into POM/QM. Lamda is 0.8125, mu is 1.666667

Resuts for one mechanic only:
Average Server Utilization: 0.49
Average number in the queue(Lq): 0.46
Average number in the system(Ls): 0.95
Average time in the queue(Wq): 0.57 34.24min 2054.21s
Average time in the system(Ws): 1.17 70.24min 4214.47
Cost (Labor + # waiting*wait cost): $19.27
Cost (Labor + # in system*wait cost): $29.02

Results for 2 Mechanics:
Average Server Utilization: 0.24
Average number in the queue(Lq): 0.03
Average number in the system(Ls): 0.52
Average time in the queue(Wq): 0.04 2.27min 136.44s
Average time in the system(Ws): 0.64 38.27min 2296.44s
Cost (Labor + # waiting*wait cost): $20.62
Cost (Labor + # in system*wait cost): $30.37

Total difference in cost is a loss of $1.35 per hour if you get a second mechanic.


I think this is close but i believe you forgot to include the info where it says no matter if the scooter is being worked on or waiting in line it is still losing 20 bucks an hour. And a full work day is 8hrs

[CUG]

Originally posted by Goo_wak_jai



I think this is close but i believe you forgot to include the info where it says no matter if the scooter is being worked on or waiting in line it is still losing 20 bucks an hour. And a full work day is 8hrs Though I appreciate the opportunity to look at the question you posted, if you know that, do the fucking work yourself homie.

[psycoticclown]

Did that.

Lamda is 6.5scootersperday/8 hours which is .8125 and mu is 1/0.6 scooters or 1.666667.

And it takes into account the money lost by being in the system, hence the average time in the system and the total cost of labor + # in system*wait cost.

[Goo_wak_jai]

Originally posted by CUG
Though I appreciate the opportunity to look at the question you posted, if you know that, do the fucking work yourself homie.

Stop bitching, I said I BELIEVE, doesn't mean i'm sure. Why would i post the question if I know how to do it? :facepalm:

[CUG]

Originally posted by Goo_wak_jai


Stop bitching, I said I BELIEVE, doesn't mean i'm sure. Why would i post the question if I know how to do it? :facepalm: I'd take Psychoclowns answer. Mine is close, but less accurate and much more rudimentary.

[Goo_wak_jai]

Originally posted by psycoticclown
You guys can't just do this by regular methods, its a waiting lines/queuing problem.

This shits easy, plug into POM/QM. Lamda is 0.8125, mu is 1.666667

Resuts for one mechanic only:
Average Server Utilization: 0.49
Average number in the queue(Lq): 0.46
Average number in the system(Ls): 0.95
Average time in the queue(Wq): 0.57 34.24min 2054.21s
Average time in the system(Ws): 1.17 70.24min 4214.47
Cost (Labor + # waiting*wait cost): $19.27
Cost (Labor + # in system*wait cost): $29.02

Results for 2 Mechanics:
Average Server Utilization: 0.24
Average number in the queue(Lq): 0.03
Average number in the system(Ls): 0.52
Average time in the queue(Wq): 0.04 2.27min 136.44s
Average time in the system(Ws): 0.64 38.27min 2296.44s
Cost (Labor + # waiting*wait cost): $20.62
Cost (Labor + # in system*wait cost): $30.37

Total difference in cost is a loss of $1.35 per hour if you get a second mechanic.

So the loss of $1.35 is that only account for the second mechanic or does that include the days loss in revenue too?

[nonlinear]

instead of blindly following the advice of these fools, your best bet is to go back to your class notes and figure the problem out yourself. your text and/or notes are a far better resource than a couple of punk kids on the internet.

[psycoticclown]

Originally posted by nonlinear
instead of blindly following the advice of these fools, your best bet is to go back to your class notes and figure the problem out yourself. your text and/or notes are a far better resource than a couple of punk kids on the internet.

:(

Anywaaaays, only helping him out cause I actually was doing an assignment on this stuff last week and it's actually really easy. Math is jr high school level and using something like POM/QM is dead easy. Actually took me more time typing my answers than getting it.

In regards to $1.35 loss in revenue, that is only the per hour cost. Everything in my answer is hourly, so loss in revenue per day should be $10.80 like CUG said. You can separate what only the mechanic costs, but it'll take you some more time.