OT-2015 Question 3 Answer-- LP

Answer available here:
https://drive.google.com/file/d/0B6PHuk6I5SxbRzdxdVRTeGg3LWM/view?usp=sharing

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Below Simplex Table is for a typical product mix problem with three products and 3 resources.  It is an optimal table. Why?

It also has alternate optimal.  Find that.                                               6 marks

	p	x1	x2	x3	s1	s2	s3	R.H.S.
P	1	0	0	0	10	15	0	7500
x3	0	0	10	1	8	-10	0	305
X1	0	1	25	0	-5	8	0	670
s3	0	0	15	0	12	5	1	320

a) Let us assume that one unit of these products or resources require one unit of storage space each. Which of the two optimum solutions obtained by you will require lesser storage than other?                                            6 marks                                                                 

b) Find one more optimal solution of the same problem.                6 marks

c) What will happen to the objective function value (increase, decrease or remain unchanged) If we choose s₁ as entering variable and do the iteration in the table given in this question.                                                    2 marks

OT-2015 Question 1 Answer -- Project Management

Answer available at:

https://drive.google.com/file/d/0B6PHuk6I5SxbSWFfRDVoLUNXMlU/view?usp=sharing

If you have a different view and feel that it may be correct than post here is as comment.

For ready reference, question is pasted here:

  Work breakdown structure of a project is given below.

Activity	Immediate Predecessor	Expected activity time (days)	Activity time variance (days)^2
a	-	10	25
b	e, h	15	30
c	g, j	9	35
d	b	12	40
e	a	8	50
f	-	7	40
g	i	20	80
h	f	15	30
i	-	5	40
j	f	10	20
k	i	10	0
l	g, j, m	28	24
m	k	7	30
n	c	10	50

a)    Draw an activity-on-arrow network diagram and find the expected project completion time.                                                                                 2+2 marks

b)    What is the probability that this project will be completed within 65 days? 

2 marks

c)    A consultant has been asked to provide his expert services in activity d. He has been asked to report to the project office to start his work on day 52 from the start day of the project. What is the probability that he will have to wait (i.e. on his arrival, activity d is not ready for start)?                              8 marks

d)    At present, activity g involves some human intelligence. Variance of 80 is quite high. Suppose, this process is automated to bring the variance to 0 but the activity time increases to 25 days. What is the probability that this changed project will get over between 46 days and 70 days from the start of the project?                                                                                      6 marks