(1) Obtain the dual of the following primal LP problem. Maximize Zx = x1 + 2x2 + x3 Subject to constraints (1) 2x1 + x2 – x3 ≤ (2) -2x1 + x2 – 5x3 ≥ -6 (3) 4x1 + x2 + x3 ≤ X1, x2,x3 ≥ 0 (2) Explain the following terms with respect to PERT / CPM. i. Dangling ii. Merge event iii. Dummy activity
[3 marks]Define Operation Research. Discuss the features of Operation Research.
[7 marks]Use the graphical method to solve the following LP problem. Maximize Z = 15x1 + 10x2 Subject to constraints, (1) 4x1 + 6x2 ≤ 360 (2) 3x1 + 0x2 ≤ 180 (3) 0x1 + 5x2 ≤ 200 X1, x2 ≥ 0.
[7 marks]Discuss the general structure and assumptions of an LP Model.
[7 marks]Solve using Simplex method: max Z = 5x1 + 10x2 + 8x3 subject to 3x + 5x + 2x ≤ 60123 4x + 4x + 4x ≤ 72123 2x + 4x + 5x ≤ 100123 and x1,x2,x3 ≥ 0
[7 marks]Determine the initial feasible solution for the following transportation problem using (1) NWCM, (2) LCM, and (3) VAM D1 D2 D3 D4 Supply S1 19 30 50 10 S2 70 30 40 60 9 S3 40 8 70 20 18 Demand 5 8 71
[14 marks]Adepartment of a company has five employees with five jobs to be performed. The time (in hours) that each man takes to perform each job is given in the effectiveness matrix. How should the job be allocated, one per employee, so as to minimize the total man-hours? Employees I II III IV V A 10 5 13 15 16 B 3 9 18 13 Jobs C 10 7 2 2 D 7 11 9 7 E 7 9 10 4
[12 marks]Describe the transportation problem with its general mathematical formulation, and Also define the following terms with reference to a transportation problem: (i) Feasible solution (ii) Basic feasible solution (iii) Optimal solution (iv) Non-degenerate basic feasible solution.
[7 marks]Explain in brief what is assignment problem? Enlist the steps of Hungarian method to solve an assignment problem.
[7 marks]What is the meaning of Inventory management and control? Explain the different inventory cost components.
[7 marks]Define job sequencing. Explain Johnson’s procedure (steps) for processing n jobs through two machines.
[7 marks]Aproject schedule has the following characteristics. Activity Time (days) 1 – 2 1 – 3 1 2 – 4 1 3 – 4 1 3 – 5 4 – 9 5 – 6 5 – 7 6 – 8 1 7 – 8 8 – 10 9 – 10
[7 marks]Construct the Network Model.
[ marks]Compute the earliest event time and latest event time.
[ marks]Determine the critical path and total project duration.
[ marks]What is ‘Inventory’? List and explain the different types of Inventories.
[7 marks]Which are the patterns of customer arrivals in a Queuing system? For a queuing system, define (i) Traffic intensity (server utilization factor) (ii) Customer arrival rate (iii) Reneging (iv) Jockeying
[7 marks]Afirm is considering the replacement of a machine, whose cost price is Rs 12,200, and its scrap value is Rs 200. From the experience the running costs are found to be as follows:2 Year 1 2 3 4 5 6 7 Running 200 500 800 1,200 1,800 2,500 3,200 4,000 Cost(Rs.) When should the machine be replaced?
[8 marks]Determine the sequence that will minimize the total elapsed time, also find idle time of all machines. Job 1 2 3 4 5 Machine 1 3 12 5 2 9 11 Machine 2 8 6 4 6 3 1 Machine 3 13 14 9 12 8 13
[6 marks]Describe the PERT/CPM network components and rules for network construction.
[7 marks]