Section A
Q1.
(a)
The costs per year (in ₹) for running a truck and its resale value are given below: Year
Running cost
Resale value 1
1,000
3,000
2
1,200
1,500
3
1,400
750
4
1,800
375
5
2,300
200
6
2,800
200
7
3,400
200
Determine at what year the replacement is due if the purchase price is ₹6,000.
(b)
Five jobs have to be processed by machines A and B in the order 'first A, then B'. The processing times of the jobs in each machine are given below: Jobs
Machine A
Machine B 1
6
3
2
2
7
3
10
8
4
4
9
5
11
5
Determine the sequence of jobs that will minimize the total elapsed time. What are the idle times for the machines?
(c) Explain the criteria—(i) optimistic, (ii) pessimistic and (iii) minimax regret in decision making under conditions of uncertainty.
(d)
The cumulative distribution function of times to failure (measured in months) for a system is F(t) = 1 - (100)/((t + 10)2), t ≥ 0
(i) What is the reliability function?
(ii) What is the failure rate as a function of time?
(iii) Does the failure rate increase or decrease?
(iv) What is MTTF?
