Q3-2018-Simulation

Question 3: Player A and Player B are playing a game by tossing of coins. Player A has a biased coin with probability of getting a head as 0.4. Similar probability for Player B coin is 0.3. Both toss their coins. Player A wins if both the outcomes are same otherwise Player B wins.

Prepare a plan to Simulate this game for ten tosses from both the players, conduct the Simulation and show the results. Summarize your result by answering which player won how many times when they tossed their coins 10 times each.

(Marks distribution: Simulation plan -- 4 marks, Simulation – 2 marks, Simulation result – 4 marks)

Answer is available at https://drive.google.com/open?id=1ak6GcvlSL_gwX6W0I-iEfOkPXc9PHHzq

Q2-2018-Linear Programming

Question 2: A paint manufacturing organization produces two qualities of paint – Premium paint and Economy paint. It requires three main chemicals for their production – Chemical A, Chemical B and Chemical C. One litre of Premium paint requires 150 units, 250 units and 200 units of Chemical A, Chemical B and Chemical C respectively. Similarly, one litre of Economy paint requires 200 units and 100 units of Chemical A and Chemical B respectively. Manufacturing process of Economy paint gives 50 units of Chemical C per litre of paint production as by-product.

Chemical A, Chemical B and Chemical C are available per day in 3000 units, 5000 units and 1000 units respectively. Premium paint gives a profit of 300 Rs./litre whereas Economy paint has a profit of Rs. 200 /litre.

a) Formulate a linear program to maximize the profit by producing the two types of paints.                                  (4 marks)

b) Use Graphical Method to recommend the optimum product mix. (Draw it on the normal answer sheet showing scale of the two axes. Approximate drawing and answer will be fine if the answer is logically correct).                                                                                             (6 marks)

c) Suppose these Chemicals are hazardous, and they should be used entirely on daily basis. You can reduce the availability of these chemicals to meet this condition. Availability of which chemicals would you reduce and by how much?                                                (10 marks)

Answer is available in a video at https://drive.google.com/file/d/1o2Q80IvsB1NbR_imSy77APbFZrmU6kY2/view?usp=sharing

Q1-2018-Project Management

Question 1: Work Breakdown Structure of a project is given below. Draw an Activity-on-Arrow diagram for this project and answer the given questions.

Activity	Immediate Predecessors	Expected activity time (Days)	Variance (Days^2)
a	None	12	25
b	a	15	0
c	f	5	107
d	b	10	29
e	None	15	55
f	None	10	76
g	c	20	45
h	e	7	116
i	a, h	10	18
j	i	6	53
k	g	8	159
l	c	15	42
m	D, I	6	10
n	j, k	10	54
o	g, l	12	65

a) Only 60 days are available for completing this project. What is the probability that it gets completed within available time?                                                                                       (6 marks)

b) An insurance organization can insure such projects against timely completion provided the probability of claim is 0.1 or lesser. How much excess (number of days of delay for which no claim is payable) should be applied in the policy to keep the probability of claim around 0.1?                                                                                                                                           (7 marks)

c) Assume that variance of all the activities in this project becomes 0. In that case what is the latest start time of activity L?                                                                                        (7 marks)

Answer is given in the video at

https://drive.google.com/open?id=1hLAdZyzchhX19kTTW2RbxCFL1PCOKutK