CS6704 RESOURCE MANAGEMENT TECHNIQUES TOPIC WISE QUESTION BANK LINEAR PROGRAMMING PROBLEMS 1) What is OR techniques? Where it can be used? 2) What is OR? List out various applications of OR. 3) Explain how operation research helps management in decision making. 4) Define following terms. i) Solution ii) Feasible solution iii) Optimum solution iv) Degenerate solution v) Basic solution 5) Explain the term. i) Non negative restrictions ii) Objective function iii) Feasible region 6) What are basic & non basic variables? 7) What is degeneracy in case of LPP? 8) Convert in dual problem & solve by Simplex Method 9) Explain the concept of Duality? How it is helpful in solving LPP? Explain with a small example. 10) How LPP is solved using graphical method? 11) An Advertising company is planning a media campaign for a client, willing to spend Rs.2000000 to promote a new fuel economy model of a pressure cooker. The client wishes to limit his campaign media to a daily newspaper, radio and prime time television .The agency‟s own research data on cost effectiveness of advertising media suggest the following: Advertising Media Cost per unit (Rs) Estimated number of housewives Exposed to each advertising unit Newspaper 20,000 1,00,000 Radio 40,000 5,00,000 Television 1,00,000 10,00,000 12) The client wishes that at least 50,000 housewives should be exposed to T.V. advertising .Also the expense on newspaper advertising must not exceed Rs.5,00,000.Formulate the problem as a linear programming problem Fatima Michael College of Engineering & Technology Fatima Michael College of Engineering & Technology
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CS6704 RESOURCE MANAGEMENT TECHNIQUES
TOPIC WISE QUESTION BANK
LINEAR PROGRAMMING PROBLEMS
1) What is OR techniques? Where it can be used?
2) What is OR? List out various applications of OR.
3) Explain how operation research helps management in decision making.
4) Define following terms.
i) Solution
ii) Feasible solution
iii) Optimum solution
iv) Degenerate solution
v) Basic solution
5) Explain the term.
i) Non negative restrictions
ii) Objective function
iii) Feasible region
6) What are basic & non basic variables?
7) What is degeneracy in case of LPP?
8) Convert in dual problem & solve by Simplex Method
9) Explain the concept of Duality? How it is helpful in solving LPP? Explain with a small example.
10) How LPP is solved using graphical method?
11) An Advertising company is planning a media campaign for a client, willing to spend Rs.2000000
to promote a new fuel economy model of a pressure cooker. The client wishes to limit his
campaign media to a daily newspaper, radio and prime time television .The agency‟s own
research data on cost effectiveness of advertising media suggest the following:
Advertising Media Cost per unit (Rs) Estimated number of housewives Exposed to each advertising unit
Newspaper 20,000 1,00,000 Radio 40,000 5,00,000 Television 1,00,000 10,00,000
12) The client wishes that at least 50,000 housewives should be exposed to T.V. advertising .Also the
expense on newspaper advertising must not exceed Rs.5,00,000.Formulate the problem as a linear
programming problem
Fatima Michael College of Engineering & Technology
Fatima Michael College of Engineering & Technology
Solve by Simplex Method.
13) Maximize (Z) = 3x1+2x2+5x3
Subject to Constraints x1+x2+x3≤9
2x1+3x2+5x3≤30
2x1-x2-x3≤8
x1 , x2,x3≥0
14) Minimize (Z) = 25x+30y
Subject to Constraints 2/3 x+1/2y≥10
1/3x+1/2y≥6
x , y≥0
15) Minimize (Z) = x1+x2
Subject to Constraints 2x1+x2≥4
x1+7x2≥7
x1 , x2≥0
16) Maximize (Z) = 2x1+3x2+4x3
Subject to Constraints x1+x2+x3≤1
x1+x2+2x3=2
3x1+2x2+x3≥4
x1 , x2,x3≥0
17) Maximize (Z) = 4x1+10x2
Subject to Constraints 2x1+x2≤10
2x1+5x2≤20
2x1+3x2≤18
x1 , x2≥0
18) Maximize (Z) = 3x1+5x2+4x3
Subject to Constraints 2x1+3x2≤8
Fatima Michael College of Engineering & Technology
Fatima Michael College of Engineering & Technology
2x1+3x2≤8
2x2+5x3≤10
3x1+2x2+4x3≤15
x1,x2,x3≥0
19) Maximize (Z) = x1+x2+x3
Subject to Constraints 3x1+2x2+x3≤3
2x1+x2+2x3≤2
x1,x2,x3 ≥0
Solve by Graphical Method
20) Maximize (Z) = 30x1+15x2
Subject to Constraints x1+3/2x2≤200
2x1+x2≤200
3x1≤200
x1 , x2≥0
21) Maximize (Z) = 5x1+7x2
Subject to Constraints x1+x2≤4
3x1+8x2≤24
10x1+7x2≤35
x1 , x2≥0
22) Minimize (Z) = 2x1+2x2
Subject to Constraints x1+3x2≤12
3x1+x1≥13
x1 -x2=3
x1 , x2≥0
23) Maximize (Z) = x1+x2
Subject to Constraints x1+2x2≤2000
Fatima Michael College of Engineering & Technology
Fatima Michael College of Engineering & Technology
x1+x2≤1500
x2≤600
x1 , x2≥0
24) Maximize (Z) = 6x1-2x2+3x3
Subject to Constraints 2x1-x2+2x3≤2
x1+4x3≤4
x2≤600
x1 , x2,x3≥0
25) Maximize (Z) = 5x1+7x2
Subject to Constraints x1+x2≤4
3x1+8x2≤24
10x1+7x2≤35
x1 , x2≥0
26) Maximize (Z) = 300x1+400x2
Subject to Constraints 5x1+4x2≤200
3x1+5x2≤150
5x1+4x2≥100
8x1+4x2≥80
x1 , x2≥0
Convert in dual problem & solve by Simplex Method
27) Minimize (Z) = 2x1+3x2
Subject to Constraints 2x1+x2≥6
x1+2x2≥4
x1 +x2≥5
x1 , x20
28) Minimize (Z) = 2x1+3x2
Subject to Constraints x1+x2≥5
Fatima Michael College of Engineering & Technology
Fatima Michael College of Engineering & Technology
x1+2x2≥6
x1 , x2≥0
29) Maximize (Z) = 3x1+2x2
Subject to Constraints x1+x2≤5
x1-x2≤2
x1 , x2≥0
30) Maximize (Z) = 6x1+7x2+3x3+5x4
Subject to Constraints 5x1+6x2-3x3+4x4≥12
x2+5x3-6x4≥10
2x1+5x2+x3+x4≥8
x1,x2,x3,x4≥0.
Fatima Michael College of Engineering & Technology
Fatima Michael College of Engineering & Technology
Transportation Problems
1) Explain Transportation problem? Explain degeneracy in transportation problem?
2) Explain in detail „Stepping stone method‟ for transportation problem with illustration.
3) Explain the steps used to solve transportation problem using MODI method.
4) What is unbalanced transportation problem? Does any extra cost required to considered in case of
such type of problem?
5) Write down the steps of North West Corner Method for solving transportation problem.
6) Explain with example how Initial Basic Feasible Solution for transportation problem using Least
Cost Method .
7) Explain the steps of Vogel‟s Approximation Method with example.
8) Solve by North West Corner Method
Plants Warehouses
Supply W1 W2 W3 W4
P1 6 2 6 12 120 P2 4 4 2 4 200 P3 13 8 7 2 80
Demand 50 80 90 180 400
9) Find the initial feasible solution for the following problem using North West Corner Method.
Fatima Michael College of Engineering & Technology
Fatima Michael College of Engineering & Technology
Activity Time in months Activity Time in months 1-2 2 4-6 3 1-3 2 5-8 1 1-4 1 6-9 5 2-5 4 7-8 4 3-6 8 8-9 3 3-7 5
Activity Predecessor Optimistic
Time (to) Most Likely
Time (tm) Pessimistic
Time (tp) A - 4 4 10 B - 1 2 9 C - 2 5 14 D A 1 4 7 E A 1 2 3 F A 1 5 9 G B,C 1 2 9 H C 4 4 4 I D 2 2 8 J E,G 6 7 8
D Dig foundation B E Fabricate steel work A F Install concrete pillars B G Place reinforcement C,D H Concrete foundation G,F I Erect steel work E J Paint steel H,I K Give finishing touch J
7) Tasks A, B, C, H, I constitute a project. The precedence relationships are A < D; A<E, B < F; D <
F,C < G, C < H; F < I, G < I
Draw a network to represent the project and find the minimum time of completion of the project
when time, in days, of each task is as follows:
Tasks A B C D E F G H I Time 8 10 8 10 16 17 18 14 9 Also identify the critical path.
8) The utility data for a network are given below. Determine the total, free, and independent