Important questions for Nov Dec 2016 CS6704 Resource Management Techniques examinations conducting by Anna University Chennai

B.E./ B.Tech. DEGREE EXAMINATION Nov Dec 2016

07th Semester / IV Year

Department of Computer Science Engineering

CS6704 Resource Management Techniques

(Regulation 2013)

Nov Dec 2016 Important Questions

Important 16 Marks Questions with answers (All five units) are listed for CS6704 Resource Management Techniques subject

1. (i).Find and discuss a Geometrical interpretation and solution as well for the following LP problem

Maximize Z = 3x1 + 5x2, subject to restrictions:

x1 + 2x2 ≤ 2000, x1 + x2 ≤ 1500, x2 ≤ 600, and x1≥0, x2≥0.

(ii). Discuss the topic on (i). No feasible solution and (ii). Unbounded solution. Give one example in each case

2. (i).Examine the following LP problem using graphical method.

Minimize Z = 2x1 + 3x2

Subject to

x1 + x2 ≥6,

7x1 + x2 ≥14

x1 and x2 ≥ 0.

(ii). List out the graphical method Procedure to solve simple linear programming problems of two decision variables.

3. (i). Consider the Linear programming model and Use Two Phase Method to solve

Maximize Z = 5x1 + 8x2

Subject to

3x1 + 2x2 ≥3,

x1 + 4x2 ≥4

x1 + x2 ≤ 5

x1 , x2 ≥ 0.

(ii) Give comparison between Minimization and Maximization problem.

4. (i).Use the Simplex method to Examine the Linear programming problem.

Maximize Z = 3x1 + 5x2

Subject to

x1 + x2 ≤ 8,

x1 + 3x2 ≤12

x1 , x2 ≥ 0.

(ii). List and explain the assumptions of Linear programming problems

5. A company manufactures two types of products P1, P2. Each product uses lathe and Milling machine. The processing time per unit of P1 on the lathe is 5 hours and on the milling machine is 4 hours. The processing time per unit of P2 on the lathe is 10 hours and on the milling machine, 4 hours. The maximum number of hours available per week on the lathe and the milling machine are 60 hours and 40 hours, respectively. Also the profit per unit of selling P1 and P2 are Rs.6.00 and Rs.8.00, respectively. Create a linear programming model to determine the production volume of each of the products such that the total profit is maximized. and also solved by simplex method

B.E./ B.Tech. DEGREE EXAMINATION Nov Dec 2016

07th Semester / IV Year

Department of Computer Science Engineering

CS6704 Resource Management Techniques

(Regulation 2013)

Nov Dec 2016 Important Questions

Important 16 Marks Questions with answers (All five units) are listed for CS6704 Resource Management Techniques subject

1. (i).Find and discuss a Geometrical interpretation and solution as well for the following LP problem

Maximize Z = 3x1 + 5x2, subject to restrictions:

x1 + 2x2 ≤ 2000, x1 + x2 ≤ 1500, x2 ≤ 600, and x1≥0, x2≥0.

(ii). Discuss the topic on (i). No feasible solution and (ii). Unbounded solution. Give one example in each case

2. (i).Examine the following LP problem using graphical method.

Minimize Z = 2x1 + 3x2

Subject to

x1 + x2 ≥6,

7x1 + x2 ≥14

x1 and x2 ≥ 0.

(ii). List out the graphical method Procedure to solve simple linear programming problems of two decision variables.

3. (i). Consider the Linear programming model and Use Two Phase Method to solve

Maximize Z = 5x1 + 8x2

Subject to

3x1 + 2x2 ≥3,

x1 + 4x2 ≥4

x1 + x2 ≤ 5

x1 , x2 ≥ 0.

(ii) Give comparison between Minimization and Maximization problem.

4. (i).Use the Simplex method to Examine the Linear programming problem.

Maximize Z = 3x1 + 5x2

Subject to

x1 + x2 ≤ 8,

x1 + 3x2 ≤12

x1 , x2 ≥ 0.

(ii). List and explain the assumptions of Linear programming problems

5. A company manufactures two types of products P1, P2. Each product uses lathe and Milling machine. The processing time per unit of P1 on the lathe is 5 hours and on the milling machine is 4 hours. The processing time per unit of P2 on the lathe is 10 hours and on the milling machine, 4 hours. The maximum number of hours available per week on the lathe and the milling machine are 60 hours and 40 hours, respectively. Also the profit per unit of selling P1 and P2 are Rs.6.00 and Rs.8.00, respectively. Create a linear programming model to determine the production volume of each of the products such that the total profit is maximized. and also solved by simplex method

6. (i).Form the dual of the following primal problem and Examine this problem.

Maximize Z = 4x1 + 10x2 + 25x3

Subject to

2x1 + 4x2 + 8x3 ≤ 25,

4x1 + 9x2 + 8x3 ≤ 30

6x1 + 8x2 + 2x3 ≤ 40

x1, x2, and x3 ≥ 0.

(ii).Identify the major relationship between primal and its dual and List out the guidelines for Dual formulation.

7. (i). Describe and Solve the following LP problem using dual simplex method.

Minimize Z = x1 + 2x2 + 3x3

Subject to

2x1 - x2 + x3 ≥ 4

x1 + x2 + 2x3 ≤ 8

x2 – x3 ≥ 2

x1 , x2 and x3 ≥ 0.

(ii). Describe the outlines of dual simplex method.

8. Given the Linear programming problem.

Maximize Z = 3x1 +5 x2

Subject to

3x1 + 2x2 ≤ 18

x1 ≤ 4, x2 ≤ 6 and x1 , x2 ≥ 0.

(i). Show that the optimum solution to the LP problem.

(ii).Illustrate the effect on the optimality of the solution when the objective function is changed to Z = 3x1 + x2.

9. What do you meant by sensitivity analysis? Discuss sensitivity analysis with respect to a) Change in the objective functions coefficients b) Adding a new constraint C) Adding a New Variable.

10. What are the jobs assignments which will minimize the cost? analyze it.

11. Solve the following integer linear programming problem using Gomary’s cutting plane method

Maximize Z = x1 + x2

Subject to

3x1 + 2x2 ≤ 5

x2 ≤ 8

x1 , x2 ≥ 0 and integers

12. Discuss Gomary’s Cutting plane method and solve it.

Maximize Z = 2x1 +2 x2

Subject to

5x1 + 3x2 ≤ 8

2x1 + 4x2 ≤ 8

x1 , x2 ≥ 0 and all integers

13. (i). Explain Bellman’s principle of optimality and give classical formulation and the dynamic programing formulation of any problem.

(ii). State the principle of optimality in dynamic programming.

Explain the basic features which characterize a dynamic programming problem

14. Estimate the shortest path from vertex A to vertx B along arcs joining various vertices lying between A and B. Length path is given.

15. (i).Describe the Concept of integer programming by a suitable example. Give any approach to solve in integer programming problem.

(ii). Describe the algorithm involved in the iterative solution to all Integer programming problem (I.P.P).

16. (i). A positive quantity b is to be divided into n parts in such a way that the product of n parts is to be maximum. Use lagrange’s multiplier technique to obtain the optimal subdivision. Explain it.

(ii). Analyze and Solve the Non LPP

Optimize Z= x1^2 + x2^2 + x3^2

Subject to

x1 + x2 +3x3 = 2 ,

5x1 + 2x2 +x3 = 5

x1 , x2 , x3 ≥ 0.

17. Solve the following Non LPP by using lagrange’s multiplier

Optimize Z= 4x1^2 +2x2^2 + x3^2 – 4x1 x2

Subject to

x1 + x2 +x3 = 15 ,

2x1 - x2 +2x3 = 20

x1 , x2 , x3 ≥ 0.

18. (i) Describe in detail about the Newton-Raphson method.

(ii) Describe in detail about the Unconstrained problems.

19. Give the solutions for NLPP by Using Kuhn-Tucker conditions

Max Z= 2x1 -x1^2 + x2

Subject to

2x1 + 3x2 ≤ 6

2x1 +x2 ≤ 4

x1 , x2 ≥ 0

20. Explain and Use Kuhn-Tucker conditions to solve NLPP

Max Z= 7x1^2-6x1+ 5x2^2

Subject to

x1 + 2x2 ≤ 10

x1 -3x2 ≤ 9

x1 , x2 ≥ 0.

21. A project consists of activities from A to H as shown in table. The immediate predecessor(s) and the duration in months of each of the activities are given in same table.

(a). Draw the project network and find the critical path and the corresponding project completion time.

(b). Also, draw a Gantt-chart/Time chart for this project and also explain this concepts.

22. Consider table below summarizing the details of a project involving 11 activities.

(a) Construct the project network.

(b) Show the expected duration and variance of each activity

(c). Find the critical path and the expected project completion time.

(d).What is the probability of completing the project on or before 25 weeks?

(e). If the probability of completing the project is 0.84, find the expected project completion time.

23. A project has the following characteristics. Construct a PERT network. Find critical path and variance for each event and also analyze it.Find the project duration at 95% probability.

24. (i) Describe in detail about the Resource allocation and Resource levelling.

(ii) Examine the following information,suggest some appropriate allocation schedule

25. (i) List out the applications areas of PERT/CPM Techniques

(ii) Write the Disadvantages of Network techniques.

(iii) Define the following terms with reference to a PERT chart:

a) Total float b) Free float

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