[wolfgang]

Someone wanted to bey a new Machine to his factory.

He found three types of machines:-

1-the first type,works 30 Minutes then stops to cool down for 5 Minutes,and works again another 30 Min.,and so on.

2-the second type,works 60 Min.,then stops for 10 Min. to cool down,and so on.

3-the third type,works 90 Min.,makes 15 Min. rest,and so on.

If each product needs 30 Min. to be completely finished with any machine,and the machine should work only 8.5 hours per day.

Which machine should he bey? why?

[Guest]

The 30 min produces 17 units; the 60 min produces 16 units; whereas the 90 min machine produces 15. This is because of truncating the 510 minutes of maximum work. If you can run the 60 min machine for 30 mins, and the 90 min machine for just 60 mins, then it all works out the same and you should just buy the cheapest one of the group.

[Guest]

Should buy 3rd type - which works 90 min then need 15 min for cooling.

As machine will work for 8.5 hrs a day then the best use of time can only be done using this machine.

if you buy 30 min then the last time you run will not complete in 8.5 hrs, same is the case for 60 min.

Calculate it as (8.5 hrs +cooling time) / (run time + cooling time).....and this should give you integer value (not in decimals)

[Guest]

In 8.5 Hours (510 Minutes):

The 30 Min Machine produces 14 Units (35 Min * 14 = 490 Min).

The 60 Min Machine produces 14 Units (70 Min * 7 = 490 Min).

The 90 Min Machine produces 15 Units (105 Min * 3 + 30 Min + 30 Min = 510 Min).

So he should buy the 90 Min Machine.

[Guest]

In 8.5 Hours (510 Minutes):

The 30 Min Machine produces 14 Units (35 Min * 14 = 490 Min).

The 60 Min Machine produces 14 Units (70 Min * 7 = 490 Min).

The 90 Min Machine produces 15 Units (105 Min * 3 + 30 Min + 30 Min = 510 Min).

So he should buy the 90 Min Machine.

Response

It says the machine should be worked for only 8.5 hours per day. The problem differentiates between work 30/60/90 mins and rest 5/10/15 mins. I took the problem to then mean, you couldn't go over 510 mins of work and that you couldn't truncate the work period either.

[Guest]

30 minute machine will complete 14 (work + rest) periods to produce 14 units and have 20 minutes of wasted time left;

the 60 minute machine will complete 7 (work + rest) periods to produce 14 units and have 20 minutes of wasted time left;

the 90 minutes machine will complete 4 (work + rest) periods and have 90 minutes left in the day, which is enough for another work cycle for a total of 5 work cycles and produce 15 units. That machine can then rest all night before the next day.

The 90 minute machine is the clear choice

[Guest]

I say machine one would be the answer. The question asks "the machine should work only 8.5 hours per day", not the total time the machine can be in use; ie work plus rest time. 8.5 hours of work time can only be accomplished by machine one, since it can work exactly 8.5 hours producing 17 units of product. The 60 minute machine would have to stop after 8 hrs of work time producing 16 units of product and the 90 minute machine would have to stop after 7.5 hrs of work time producing 15 units of product.

Edited December 23, 2010 by toomuchtime

[Guest]

510 mins total

O/p of m/c#1: [510 / 35] * 1 = 14 * 1 = 14 (in 485 mins)

O/p of m/c#2: [510 / 70] * 2 = 7 * 2 = 14 (in 480 mins)

O/p of m/c#3: [510 / 105] * 3 = 4 * 3 = 14 (in 405 mins) beginning at 420th min it can start production again so total production will be 17 units.

Hence, buy machine 3.

[Guest]

The 90 minutes machine will complete 4 (work + rest) periods and have 90 minutes left in the day, which is enough for another work cycle for a total of 5 work cycles and produce 15 units. That machine can then rest all night before the next day.

The 90 minute machine is the clear choice

For those that argue that the machine can work for 8.5 hours without taking the rest into consideration I would argue that we would be looking at stringing numerous 8.5 hour days together which still supports my logic on purchasing the 90 minute machine.

[Guest]

I would have thought it was the 1st machine.

This is because if each products needs 30mins, then you only want your machine to run for 30mins then cool down so you can start again. Hope that makes sense.

Although you could go for the second just in case it takes a little longer.

Just one question, does the machine need to be reset once each product has been completed?

Edited December 23, 2010 by theboyB0B

[wolfgang]

In 8.5 Hours (510 Minutes):

The 30 Min Machine produces 14 Units (35 Min * 14 = 490 Min).

The 60 Min Machine produces 14 Units (70 Min * 7 = 490 Min).

The 90 Min Machine produces 15 Units (105 Min * 3 + 30 Min + 30 Min = 510 Min).

So he should buy the 90 Min Machine.

[Guest]

This is my thoughts using math.

8.5hrs=60*8.5=510min M1=14U M2=14U M3=15U You should get Machine 3.

[wolfgang]

This is my thoughts using math.

8.5hrs=60*8.5=510min M1=14U M2=14U M3=15U You should get Machine 3.

Thats right...good