Question: Q1: Solve the following problem graphically: Maximize Z=3x=9 Subject to the constraints: x+3y = 60 x+y2 10 XS where xy20 (25 Marks) Q2: The below

Q1: Solve the following problem graphically: Maximize Z=3x=9 Subject to the constraints: x+3y = 60 x+y2 10 XS where xy20 (25 Marks) Q2: The below table defines the activities within a small project. (1) Draw the network diagram, (ii) Calculate the minimum overall project completion time and identify which activities are critical (critical path). Activity Nodes Duration time B D E F G 1 H J K L M 1-2 1-4 2-3 2-5 4-7 5-8 3-6 7-10 6-9 8-11 9-11 10-12 11-12 + 2 2 + 4 3 5 3 7 2 6 5 5 (25 Marks) Q3: Solve the following Linear programming problem model using simplex method: Maximize 2-3x1 - x2 ST. 2x1 + x222 X1+ 3x2 53 X24 where x1, x22 (25 Marks) Q4: Suppose that an engineer has five jobs that can be performed on any of five machines. The cost (8) of completing each job-machine combination is presented in the table below. Find the optimal assignment where the machine M4 does not take up the task J4. Job Machine JI J2 J3 JS MI M2 M3 M4 10 5 15 20 2 10 5 15 15 14 13 15 2 7 9 + 15 8 (25 Marks) 2-1 Q5(A): Answer the following multiple choice 1. In an assignment problem involving 4 workers and 4 jobs, total number of assignments possible are A. 25 B. 10 C. 15 D. 4 2. In Critical Path of CPM used in project planning techniques indicates - A. time require for the completion of the project B. delays in the project C. early start and late end of the project D. none of them 3. PERT analysis is based on? A. optimistic time B. pessimistic time C. most likely time D. all of them 4. An event is indicated on the network by a number enclosed in A. a circle B. a square C. a triangle D. all of them 5. Graphical optimal value for Z can be obtained from A. Corner points of feasible region C. Both a and c B. corner points of the solution region D. none of the above 6. The solution to LPP give below is, Max Z = 3x1 +14x2 subject to x1 - x2 21, - x1 + x2 2 2 where x1, x2 20 A. Unbounded solution B. Max Z-14 C. Max Z=3 D. Infeasible solution (B): Solve the following Linear Programming Problem graphically to find the maximum value of Objective function z = 4x + 2y Subject to the constraints: x+2y 24 3x + y 27 -x +2y 57 Where, x, y20

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