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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:2013
QUESTION ONE (30 MARKS)
a) State four advantages of linear programming in decision making. (4 Marks) b) Explain the concept of duality in linear programming. (3 Marks) c) Find the dual of the problem = 51 + 22 1 + 22 5 21 2 12 1 + 32 4 1 0,2 0 (5 Marks) d) Convert the linear program to canonical form. = 3 + 4 + 2 12 2 3 18 , 0 (2 Marks) e) Arrivals at a service counter are considered Poisson with an average time of 10 minutes between arrivals. The length of service is assumed to be distributed exponentially with a mean 3 minutes. i. What is the probability that a person arriving at the counter will have to wait? (4 Marks) ii. What is the average length of queues that form from time to time? (4 Marks)
2
f) Mombasa publishers a leading manufacturer of books publishes the books in 3 printing machines that are distributed to 4 regions. The distribution costs per book, the production capacity in each plant and demand for books in each region is given below.
Destination Source Malindi Kwale Voi Kilifi Supply P1 21 32 52 12 7000 P2 72 32 42 62 9000 P3 42 10 72 22 18000 Demand 5000 8000 7000 1400
(8 Marks)
QUESTION TWO (20 MARKS)
a) A small project has been broken down into 10 activities A-J with the following predecessors and duration. Activity predecessor Duration(weeks) A - 5 B - 7 C A,B 8 D - 10 E C 10 F B 5 G C,F,H 8 H D 12 I D 7 J I 9 Draw the network diagram and identify the critical path. (10 Marks) b) i) What is Economic Order quantity? (10 Marks) ii) A manufacturer has to supply his customers with 2400 units of his product every year. This demand is fixed and known. Since the unit is used by the customer in an assembly line operation and the customer has no storage space for units, the manufacturer must supply a days requirements each day. If the manufacturer fails to apply the required units the shortage cost is 2 shillings per unit per month and the set up cost per run is 3500 shillings. Determine; i. Optimum run size. (4 Marks) ii. Optimum level of inventory at the beginning of any period. (4 Marks)
3
QUESTION THREE (20 MARKS)
a) Explain the difference between transport and assignment models. (2 Marks) b) A distribution system has the following transportation schedule. Warehouse 1 2 3 Supply
Factory
A 10 7 8 45 B 15 12 9 15 C 7 8 12 40 Demand 25 55 20 100 Determine the initial feasible solution by the least cost method. (8 Marks) c) products. Production costs differ from one plant to another as to the costs of raw materials. Given the production data below, assign the products to plants so as to realize maximum profit and state the maximum profit. (10 Marks) Products A B C D
Plants
1 1 8 4 1 2 5 7 6 5 3 3 5 4 2 4 3 1 6 3
QUESTION FOUR (20 MARKS)
a) Set up the starting simplex table for the L.P.P and show that the starting solution is degenerate. (5 Marks) = 3 + 9 + 2 4 + 4 8 (,) 0 b) A firm produces three types of pumps A, B, C each of which requires the four processes of turning, drilling, assembling and testing Process in (hours)per pump Pump type Turning Drilling Assembling Testing Profit/pump (ksh) A 2 1 3 4 84 B 1 1 4 3 72 C 1 1 2 2 52 Total available time (hours per week) 98 60 145 160
4
From the information given in the table, apply simplex method to determine the weekly output of each type of pump to maximize profit and state the maximum profit. (15 Marks)
QUESTION FIVE (20 MARKS)
a) Explain the minimax – maxmin principle in Game Theory. (4 Marks) b) Consider the pay-off matrix for two players A and B given;
1 2
1 7 6 2
2
1
Calculate the value of the game to A. (4 Marks) c) State and explain 3 three assumptions of Game Theory. (6 Marks) d) State and explain 3 limitations of games in competition. (6 Marks)
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