Hbc2122:Operations Research Question Paper
Hbc2122:Operations Research
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2014
QUESTION ONE (30 MARKS)
(a) (i) State two advantages of the PERT method of Network analysis. (2 Marks) (ii) A project has the following characteristics Activity Preceding activity Time Estimates in weeks A None 3 7 11 B None 2 2.5 6 C A 2 3 4 D A 6 7 14 E A 2 3 4 F C 2.5 3 3.5 G D 2.5 4 5.5 H B, E 4.5 5.5 9.5 I H 1 2 3 J F, G, I 1 2 3 Required i. Draw the PERT network diagram. (3 Marks) ii. Identify the critical path. (1 Mark) iii. Determine the mean project completion time. (1 Mark)
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iv. Find the probability that the project is completed in 20 weeks. (3 Marks)
(b) A company employs service engineers based at various locations throughout the country the service have been received and the company finds that four engineers are available. The distance in miles each of the engineers is from the various customers is given in the following table and the company wishes to assign engineers to customers to minimize the total distance to be travelled.
W X Y Z Alf 25 18 23 14 Bill 38 15 53 23 Charlie 15 17 41 30 Dave 26 28 36 29 (i) Find out how the engineers should be dispatched so as to minimize the total mileage travelled. (8 Marks) (ii) Calculate the total mileage travelled. (2 Marks)
(c) The Waffles Manufacturing Company has a current transportation schedule which is being questioned by the top management as to whether or not it is optimal. The firm has three factories and five warehouses. The necessary data in terms of unit transportation cost in shillings, factory capacities and warehouse requirements are given below.
Factories Warehouse A B C Warehouse requirements 1 50 40 80 400 2 80 70 40 400 3 60 70 60 500 4 60 60 60 400 5 30 50 40 800 Factory availability 800 600 110
Find a feasible solution using North-west corner method. (5 Marks)
(d) Find the dual of
0, 35 52 65 yx yx yxtosubject yxzMazimize
(5 Marks)
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QUESTION TWO (20 MARKS)
(a) Explain each of the following terms as used in Linear programming. (i) Feasible solution (1 Mark) (ii) Optimal solution (1 Mark) (iii) Optimal value (1 Mark)
(b) A company can produce three products A, B and C. The products yield a contribution of in the next period. Each unit of the products uses 2, 3 and 1 hour respectively of the machines capacity. There are only 150 units available in the period of a special component which is used singly in products A and C. 200kg only of a special alloy is available in the period. Product A uses 2kg per unit and C uses 4kg per unit. There is an agreement with a trade association to produce no more than 50 units of product B in the period Required Use simplex method to find out the production plan which maximizes contribution. (17 Marks)
QUESTION THREE (20 MARKS)
(a) (i) Discuss any three management applications of Linear programming. (3 Marks) (ii) The manager of an oil company refinery must decide the optimal mix of the possible blending process of which the input and output per production run are as under. Input (units) Output (units Process Grade A Grade B Gasoline X Gasoline Y 1 5 3 5 8 2 4 5 4 4
The maximum amounts available of Grade A and B are 200 units and 150 units respectively. Market requirements show that at least 100 units of gasoline X and 80 units of gasoline Y must be produced. The profits per production run for process 1 and process 2 are Rs.300 and Rs. 400 respectively. Formulate the underlying Linear program. (5 Marks)
(b) The following is a transportation problem with cost-coefficients Destination R S T Supply Source A 1 2 3 100 B 4 1 5 110 Demand 80 120 60
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Find the optimal solution using the stepping stone method. (12 Marks)
QUESTION FOUR (20 MARKS)
(a) Find the initial basis feasible solution to the following transportation problem using Vogels approximation method. (10 Marks)
To M 1 M2 M3 M4 F1 3 2 4 1 20 F2 2 4 5 3 15 From F3 3 5 2 6 25 Supply F4 4 3 1 4 40 30 20 25 25 Demand
(b) Five wagons are available at stations 1, 2, 3, 4 and 5. These are required at five stations I, II, III, IV and V. The mileages between various stations are given by the table below
I II III IV V 1 10 5 9 18 11 2 13 9 6 12 14 3 3 2 5 4 5 4 18 9 12 17 15 5 11 6 14 19 10 Determine how the wagons should be transported in order to minimize the total mileage covered. (10 Marks)
QUESTION FIVE (20 MARKS)
(a) Briefly discuss any three elements of a queuing system. (6 Marks) (b) With the aid of a well labeled diagram, discuss the major constituents of a queuing system. (7 Marks) (c) A person repairing radios finds that the time spent on the radio sets has exponential distribution with mean 20 minutes. If the radios are repaired in the order in which they come in and their arrival is approximately Poisson with an average rate of 15 for 8 hours a day, find the number of jobs that are ahead of the average set just brought in. (4 Marks) (d) Discuss three advantages of the simulation technique. (3 Marks)
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