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Total No. of Questions : 8
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Roll No...................................
MMIE-104
M.E./M.Tech., I Semester
Examination, November 2022
Quantitative Techniques In Management
Time : Three Hours
Maximum Marks : 70
Note : i) Attempt any five questions.
ii) All questions carry equal marks.
1. a)
Convert the following LPP into standard form
maximize u = 2x + 6y + 5z'
Subject to the conditions
5x – 2y + 3z ≤ 9, x + y + z ≥ 5; x + 2y = 7
and the non negativity conditions x ≥ 0, y ≥ 0, z ≥ 0.
b)
Differentiate between general LPP and standard LPP.
2. a)
Solve the following LPP by resolving degeneracy:
maximize z = 5x + 3y
x + y ≤ 2,
5x + 2y ≤ 10
53x + 8y ≤ 12
and the non negativity conditions x ≥ 0, y ≥ 0, z ≥ 0.
b)
Explain the method of dual simplex algorithm. What are the essential difference between simplex method and dual simplex method.
3. a)
Determine the initial basic feasible solution to the following transportation problem using north west corner method:
b)
Find the optimal solution of the following LPP
maximize z = 3x + 5y
Subject to the conditions x ≤ 4, y ≤ 6, 3x + 2y ≤ 18
and the non negativity conditions x ≥ 0, y ≥ 0.
What happens to this optimal solution if the objective function is changed to z = 3x + y
4. a)
Discuss the effect of changing a component cij of price vector c on the optimal solution of LPP.
b)
In the following LPP
maximize z = 3x + 5y
Subject to the conditions x + y ≤ 1, 2x + 3y ≤ 1
and the non negativity conditions x ≥ 0, y ≥ 0. Obtain the variations in cj (j = 1,2) which are permitted without changing the optimal solution.
5. a)
Solve the following minimal assignment problem
6. a)
Describe Queuing models. People arrive at a cinema ticket booth in a Poisson distribution with an arrival rate of 25 per hour. Service time is exponentially distributed with an average time of 2 minutes. Calculate the mean number in the waiting line, the mean waiting time, the mean number in the system, the mean time in the system and the utilization factor?
b)
What is the game theory? Describe various types of games.
7.
Solve the following 2×2 game
i)
Does it have a saddle point?
ii)
Is it correct to state that the value of G is 5<G<6?
iii)
Determine the frequency of optimum strategies by matrix oddment method and find the value of game.
8. a)
Explain clearly the various ingredients of decision problems. What are the basic steps of decision making process?
b)
Describe Decision tree analysis.