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Hbc2122:Operations Research Question Paper
Hbc2122:Operations Research
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2011
QUESTION ONE (30 MARKS)
(a) Define the following terms (i) Operation Research (2 Marks) (ii) Mathematical Model (2 Marks) (iii)Degeneracy (2 Marks) (iv) Queuing Model (2 Marks) (b) State two objectives of inventory control. (2 Marks) (c) Define simulation, hence briefly discuss the steps in the simulation process. (4 Marks) (d) Find the dual of the following programming problem. Maximize: = 2 + 3 + 4 + 3 + 6
Subject to: + 2 + 5 4 ,, 0 (e) Differentiate between (i) The primal and standard forms of a linear programming model using examples. (3 Marks) (ii) Transport problem and the assignment problem. (4 Marks) (f) In the production of 2 types of toys, a factory uses 3 machines A, B and C. The time required to produce the first type of toy is 6hours, 8hours and 12 hours in machine A, B
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and C respectively. The time required to make the second type of toy is 8 hours, 4 hours and 4 hours in machines A, B and C respectively. The maximum available time (in hours) for the machines A, B and C are 380, 300 and 400 respectively. The profit on the first type of toy is 5 dollars while on the second type of toy is 3 dollars. Formulate a linear programming problem to find the number of toys of each type that should be produced to get maximum profit. (4 Marks)
(g) Define the term saddle point (1 Mark)
(h) Consider the game of matching coins. Two players, A and B put down a coin. If coins match (i.e., both are heads or both are tails) A gets rewarded, otherwise B. However B. However, matching on heads gives a double premium. Obtain the best strategies for both players and the value of game. (3 Marks)
QUESTION TWO (20 MARKS)
(a) State and explain the four classifications of the inventory related costs. (4 Marks) (b) Newtech hardware company sells hardware items. Consider the following information
Annual Sales = Ksh.10,000
Ordering cost = Ksh.0.25 per order
Carrying cost = 12.5% average inventory values.
Find the optimal
(i) Order size (2 Marks) (ii) Number of orders per year (2 Marks) (iii)Cycle period (2 Marks) (c) State and discuss the components of the Queuing system. (2 Mark) (d) Universal Bank is considering opening a drive in window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The teller whom it is considering to staff the window can serve customers at the rate of one every three minutes. Assuming Poisson arrivals and exponential service, find the average (i) Number in the waiting line (2 Marks) (ii) Number in the system (2 Marks) (iii)Waiting time in line (2 Marks) (iv) Waiting time in the system (2 Marks)
QUESTION THREE (20 MARKS)
(a) State two advantages and two disadvantages of linear programming. (4 Marks) (b) Solve the following LP problem graphically (6 Marks)
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(c) Use the simplex method to solve the following LPP (10 Marks)
QUESTION FOUR (20 MARKS)
(a) (i) Define sensitivity analysis (1 Marks) (ii) State and briefly discuss the direct information acquired from the simplex method using the sensitivity analysis, hence extract the same information from the final optimal table below. (7 Marks)
Basis X1 X2 X3 X4 S1 S2 S3 Check Z 0 0.38 0 1.5 1.88 0 0.48 99.03 S2 0 -9.2 0 1.77 -7.81 1 0.61 46.12 X1 1 0.73 0 -0.67 1.42 0 0.15 7.23 X3 0 0.27 1 1.69 -0.42 0 0.15 7.88
QUESTION FIVE (20 MARKS)
(a) Differentiate between North West Corner method, the Least Cost method and Vogel Approximation method. (3 Marks) (b) Write down a schematic representation of any transport model, hence state the main objectives of any transport model. (5 Marks) (c) A given transportation problem has four demand destinations A, B, C and D and three supply locations (1, 2, and 3). The unit cost, demand and supply requirements are as follows:
4 + 2 80 + 2 50 , 0
Maximize profit $: = 10 + 8
Subject to :
6 + 20 400 10 + 15 450 , 0
Maximize: Z = 45 + 80
Subject to :
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DESTINATIONS SUPPY
SOURCES
A B C D
1 5 12 7 10 50
2 4 6 7 6 50 3 2 8 5 3 60 DEMAND 40 20 30 3 160
Let be the number of units of commodity transported from ith supply location( = 1,2,3) into jth demand destination = 1,2,3,4. Formulate mathematically the transport problem. (6 Marks)
(d) Luminous lamps have three factories: 12 3 with production capacity 30, 50 and 20 units per week respectively. These units are to be shipped to four warehouses 1,2 3 and 4 with requirement 20, 40, 30 and 10 units per week respectively. The transport cost (in dollars) per unit between factories and warehouses are given below.
Factory Warehouse Supply W1 W2 W3 W4 F1 1 2 1 4 F2 3 3 2 1 F3 4 2 5 9 Demand 20 40 30 10
Use the North West Corner method to find the initial basic feasible solution for the given transport problem. (6 Marks)
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