What is Operation Research? Explain features and application of OR.
[7 marks]What is Linear Programming? Explain the basic components of an LP model. Also state its assumptions.
[7 marks]Construct the dual of the problem. Maximize Z=3X +5x12 Subject to Constraints, 6X +6X ≤ 55,12 8X +2X ≤ 30,12 5X -3X ≤ 18,12 X ≤ 282 Where X ≥ 0, X ≥ 0.12
[7 marks]Use the graphical method to solve the following LP problem Minimize Z=20X +10X12 Subject to constraints, X +2X ≤ 40,12 3 X + X ≥ 30,12 4 X +3 X ≥ 60,12 And X , X ≥ 0.12
[7 marks]Use the simplex method to find the optimal solutions of the following LP Problem. Maximize z =5x +3x12 x +2x ≤ 10,12 x -2x ≤ 8,12 And x , x ≥ 0.12
[7 marks]Solve the assignment problem At the head office of a company there are five registration counters. Five persons are available for service. How should the counters be assigned to persons so as to maximize the profit? Person A B C D E Counter
[7 marks]Discuss the various types of inventories in detail.
[7 marks]The production department for a company requires 4000 kg of raw material for manufacturing a particular item per year. The cost of placing an order is Rs. 40 and the cost of carrying inventory is 25% of the investment of the inventories. The purchase price is Rs. 10per kg. Determine the ordering policy for the purchase of raw material.
[7 marks]Find the Initial basic feasible solution to the following transportation problem using Page 1 of Vogel’s Approximation. Destination D1 D2 D3 D4 Supply Source O1 3 1 7 4 300 O2 2 6 5 9 400 O3 8 3 3 2 500 Demand 250 350 400 200 1200
[2 marks]The cost of a machine is Rs.6100 and its scrap value is Rs.100.The maintenance costs found from experience are as follows: Year 1 2 3 4 5 6 7 Maintenance cost(Rs) 100 250 400 600 900 1200 1600 2000 When should the machine be replaced?
[8 marks]Asuper market has a single cashier. During the peak hours, customers arrive at a rate of 20 customers per hour. The average no of customers that can be processed by the cashier is 24 per hour. Find
[7 marks]The probability that the cashier is idle. (ii) The average no of customers in the queue system. (iii)The average time a customer spends in the system. (iv)The average time a customer spends in queue.
[ marks]The any time a customer spends in the queue waiting for service.
[ marks]Solve the payoff matrix. Determine the best strategies for players Aand Band the value of the game. B’s Strategy B1 B2 B3 B4 B5 A1 8 10 -3 -8 -12 A2 3 6 0 6 A’s A3 7 5 -2 -8 17 Strategy A4 -11 12 -10 10 A5 -7 0 0 6
[2 marks]Define: Simulation. State the advantages and disadvantages of simulation.
[7 marks]Explain the difference between PERT and CPM.
[7 marks]There are four jobs to be completed. Each job must go through machines M1, M2, M3 in the order M1 – M2 – M3. Processing time in hours is given below. Determine the minimum elapsed time and idle time for Machine M1. JOBS A B C D M1 5 8 7 M2 6 7 2 M3 7 8 10 9
[5 marks]Asmall project is composed of seven activities as given below: Activity A B C D E F G Preceding Activity --- --- A A,B C,D E C,D to (days) 2 3 5 4 5 2 tm (days) 4 5 7 7 9 4 tp (days) 6 7 9 10 14 6 9 1. Draw project network 2. Find Critical Path, Expected duration, standard deviation and variance of all activities.
[6 marks]What is the main objective of sequencing problem? State the assumptions generally made while dealing with sequencing problems. Page 2 of
[2 marks]