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There are two machines that break down with a probability of

Sent to Math Experts January 11 2009 at 3:24 AM
   

There are two machines that break down with a probability of 0.2 (each) per day. This is a binomial probability of 0, 1 or 2 failures per day with probabilities of .64, .32 and .04 respectively. You can hire one or two repairmen at a cost of $50 per man per day. Machine downtime costs you $80 per hour if one machine is down but $120 per hour if both machines are down. One man can fix a machine in four hours and two men working together can fix a machine in three hours.

1. How many repairmen should you hire and what is the expected cost?

a. 0
b. 1
c. 2

2. The total maintenance cost (including downtime cost) in the case of two repairmen on duty is:

a. $96
b. $134
c. $150
d. $191
e. None of these.

 

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Level: 1; Subject: Management Science

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January 11 2009 at 5:32 AM (2 hours and 8 minutes and 44 seconds later)
         
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Hello!

 

1. b

 

The expected cost (total maintenance) is about $184 per day ( Downtime cost $134 + Repairman cost $50)

 

2. e

 

The downtime cost is $96 in case of two repairmen and their cost is $100. Therefore the total maintenance cost is $196.

 

Ask in case of further queries.

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Thanks.

 




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January 11 2009 at 5:36 AM (3 minutes and 10 seconds later)
         
What formula did you used?

Expected Value or what?
Answer
January 11 2009 at 6:18 AM (41 minutes and 55 seconds later)
         

I have given expeceted cost in both the cases.

I will give the solution in my next reply.

 

 




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January 11 2009 at 6:46 AM (28 minutes and 28 seconds later)
         

 

Let A= event of 0 failure per day

B= event of 1 failure per day

C= event of 2 failure per day

Given P(A)=.64

P(B)=.32

P(C)=.04

 

If we hire 1 repairman then his cost is $50

 

Maintenance Cost= (Downtime cost when 0 machine fails)+(Downtime cost when 1 machine fails)+(Downtime cost when 2 machine fails)

 

= 0 + P(B)*(time for repair* cost) + P(C)*(time for repair when both machines down* cost + time when one machine repaired)

 

=0 +.32* 4 *80 + .04 *(4*120 + 4*80)

=134.4

 

Expected Cost = Downtime cost + Repairman Cost

=134.4+ 50

=$184

 

If we hire 2 repairmen then their cost = 2*50= $100

 

Maintenance Cost= (Downtime cost when 0 machine fails)+(Downtime cost when 1 machine fails)+(Downtime cost when 2 machine fails)

 

Maintenance cost = 0 + .32*3*80(both men repair together) + .04*(4*120)(both men repair a machine each)

= $96

 

Total Expected Cost = $100+$96

=$196

 

With No repairman available even when one machine breaks down for 8 hours

Downtime Cost becomes = .32*8*80

=$204

which exceeds the total expected cost with 1/2 repairmen on duty

 

Thus 1 repairmen should be hired and the expected values are as calculated above.

 

 

 




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