State the definition of Operation Research. Also explain the phases of Operation Research.
[7 marks]What is LPP? Acompany manufacturer 3 types of pats which use precious metals platinum and gold. Due to shortage of these precious metals, the government regulates the amount that may be used per day. The relevant data with respect to supply, requirements, and profits are summarized in the table as follows: Platinum Gold required/unit Product Profit/unit (Rs) required/unit (gms) (gms) A 2 3 500 B 4 2 600 C 6 4 1200 Daily allotment of platinum and gold are 160gm and 120gm respectively. How should the company divided the supply of scarce precious metals? Formulate it as a linear programing problem.
[7 marks]Solve the following LPP by graphical method Minimize Z=40 + 24 Total Cost x1 x2 Subject to 20x + 50x > 4800 Phosphate Requirement12 80x + 50x > 7200 Nitrogen Requirement12 x ,x >
[12 marks]Solve following LPP using Simplex Method: Minimize Z=40x + 35x Profit12 Subject to 2x + 3x < 60 Raw Material Constrain12 4x + 3x < 96 Labor Hours Constrain12 x ,x >
[12 marks]Solve following LPP by Big-Mmethod. Minimize Z=120x + 60x12 Subject to 20x + 30x > 90012 40x + 30x > 120012 x ,x >
[12 marks]Formulate classical transportation problem mathematically or provide transportation model
[7 marks]Solve below example using North West Corner rule and the Least Cost method of obtaining an initial feasible solution for a transportation problem. To P Q R S Supply From A 12 10 12 13 500 B 7 11 8 14 300 C 6 16 11 7 200 Demand 180 150 350 320 1000
[7 marks]Explain primal and dual relationship.
[7 marks]Consider the following transportation problem. Obtain an initial feasible solution for a transportation problem by VAM method. To P Q R S Supply From A 12 10 12 13 500 B 7 11 8 14 300 C 6 16 11 7 200 Demand 180 150 350 320 1000
[7 marks]Solve the following assignment problem by (a) enumeration method and (b) Hungarian assignment method Time (in minutes) Worker Job 1 Job 2 Job A 4 2 B 8 5 C 4 5
[6 marks]Explain the difference between PERT and CPM
[7 marks]Adispatcher of the police department has received four requests for police assistance. Currently six patrol cars are available for assignment and the estimated response time (in minutes) are show in the table that follows: Patrol unit Incident I 6 5 3 4 5 II 8 6 2 3 7 II 4 4 7 6 5 IV 3 7 9 8 4
[7 marks]Which patrol units should respond?
[ marks]What will be the average response time?
[ marks]Draw a network from the below given information and determine the critical path Activity Immediate Predecessor(s) Activity Immediate Predecessor(s) A - G C,F B - H B C - I E,H D A,B J E,H E B K C,D,F,J F B L K
[7 marks]What is queuing theory? Explain general structure of the queuing system.
[7 marks]What is simulation? Explain advantages, disadvantages and application of simulation.
[7 marks]Afirm is using a machine whose purchase price is Rs. 13000. The installation charges amount Rs. 3600 and the machine has a scrap value of Rs. 1600 because the firm has a monopoly of this type of work. The maintenance cost in various years is given in the following table. Year 1 2 3 4 5 6 7 8 9 Cost (Rs.) 250 750 1000 1500 2100 2900 4000 4800 6000 The firm wants to determine after how many years should the machine be replaced on economic consideration assuming that the machine replacement can be done only at the year ends.
[7 marks]Arrivals at the telephone booth are considered to be Poisson with an average time of 10minutes between one arrival and the next. The length of a phone call is assumed to be distributed exponentially with mean 3 minutes. Find
[7 marks]The probability that an arrival finds that four persons are waiting for their turn ; (ii) The average number of persons waiting and making telephone calls ; and (iii) The average length of the queue that is formed from time to time.2
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