Hbc2122:Operations Research Question Paper
Hbc2122:Operations Research
Course:Bachelor Of Commerce
Institution: Meru University Of Science And Technology question papers
Exam Year:2012
QUESTION ONE (30 MARKS)
a) Explain five assumptions of linear programming in decision making. (5 Marks) b) A manufacturer produces two types of drinks, lager and stout. Lager is sold at a profit of three shillings per unit and stout four shillings per unit. The manufacturer wishes to establish the weekly production plan which maximizes profit.
Production data are as follows
Machine hours/unit Labour hours/unit Materials (Kgs) Lager 4 4 1 Stout 2 6 1 Total available per week 100 180 40
Because of a trade agreement sales of lager are limited to a weekly maximum of 20 units and to honour an agreement with an old established customer at least 10 units of stout must be sold per week. Formulate the L.P model governing these data and solve the problem graphically to determine the maximum profit. (9 Marks)
c) Explain the concept of duality in linear programming. (2 Marks) d) Consider the primal problem Minimize ??0 = 5??1 + 2??2 Subject to ??1 + 2??2 = 5 2??1 - ??2 = 12 ??1 + 3??2 = 4
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??1 = 0,??2 = 0 Write down its dual problem. (4 Marks) e) Explain the concept of degeneracy in linear programming. (2 Marks) f) Consider the LPP Minimize ?? = 3??1 + 9??2 Subject to ??1 + 4??2 = 8 ??1 + 2??2 = 4 ??1,??2 = 0 Set up the starting simplest fob lean and show that the starting basic solution is degenerate. (5 Marks) g) State three components of the queuing system. (3 Marks)
QUESTION TWO (20 MARKS)
a) The demand rate of particular items is 12000 units per year. The set up cost per run is Ksh. 350 and holding cost is Ksh. 0.20 per unit per month. If no shortages are allowed and the replacement is instantaneous, determine; i. Optimum run size. (2 Marks) ii. Optimum scheduling period. (2 Marks) iii. Minimum total expected cost. (2 Marks) b) A firm produces three types of pumps, A,B, C each of which requires the four processes of turning, drilling, assembling and testing
Pump type Process time (hours) per pump Profit per pump (Ksh) Turning Drilling Assembling Testing 84 A 2 1 3 4 72 B 1 1 4 3 52 C 2 1 2 2 Total Available time (h/weeks) 98 60 145 160
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. (14 Marks)
QUESTION THREE (20 MARKS)
a) Explain the following terms as used in network analysis. (8 Marks) i. A path ii. A loop iii. Connected network iv. A tree
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b) The following table shows the jobs of a project with their duration in days Jobs 1-2 1-3 1-4 2-5 3-7 4-6 5-7 5-8 6-7 6-9 7-10 8-10 9-10 10-11 11-12 duration 10 8 9 8 16 7 7 7 8 5 12 10 15 8 5
Draw the network diagram and find the critical path. (12 Marks)
QUESTION FOUR (20 MARKS)
a) Explain the difference between transport and assignment models. (2 Marks) b) A distribution system has the following transportation schedule. Warehouse
Factory
I II III Supply A 10 7 8 45 B 15 12 9 15 C 7 8 12 40 Demand 25 55 20 100
find the optimal solution. (7 Marks) c) A sales manager wants to deploy 5 salesmen all of different abilities to 5 districts. The manger estimates that the sales per be as follows DISTRICT SALES MAN A B C D E 1 32 38 40 28 40 2 40 24 28 21 36 3 41 27 33 30 37 4 22 38 41 36 36 5 29 33 40 35 39
Find the assignment of salesman to the districts that will result in maximum sales and calculate the sales revenue generated by the assignment. (11 Marks)
QUESTION FIVE (20 MARKS)
a) Explain the minimax maxmin principle in game theory. (2 Marks) b) In a game of matching coins with the players, suppose A wins one nit of value when there are two heads, wins nothing units of value when there are two tails and two 0.5 units of value when there is one head and one tail. Determine the pay-off matrix, the best strategies for each player and the value of the fame to A. (8 marks)
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c) A mobile fast food canteen serves college students over lunch time. On busy days, the canteen receives students at a rate of 140 per hour. Each students order takes 25 seconds to process. Assuming that students arrive in a Poisson manner and the service rate is exponential (?? ?? 1) determine, (10 Marks) i. Proportion of the time that rates are busy. ii. Average number of students in the system. iii. Average number of students in queue. iv. Average time spent in the system v. Average time spent in the queue.
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