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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) Discuss any three basic elements of Queing Model. (6 Marks) (b) Find the dual linear program of the following primal
= 51 + 62 : 1 + 22 = 5 1 + 52 3 41 + 72 8 1 ,2 0 (6 Marks) (c) Solve the following L.P.P by simplex method = 31 + 22 : 41 + 32 12 41 + 2 8 41 2 8 1, 2 0 (10 Marks)
2
(d) Consider the following information Activity Immediate Predecessors Duration A None 2 B None 3 C A 1 D B 4 E C,D 3 F D 1 G E 2 H F 3
Draw the project network and find the critical path. (8 Marks)
QUESTION TWO – (20 MARKS)
A firm operates 3 plants each of which produces animal feeds in 3 outputs A, B and C. The hourly output in tones of the plants is as follows:
A B C Plant I 10 20 30 Plant II 20 10 10 Plant III 30 20 10
On a particular day, this company receives an order to supply 1000 tonnes of feed A, 800 tonnes of feed B and 500 tonnes of feed C. The cost per hour of running the three plants are 40, 50 and 60 dollars respectively. Assuming that the plant will run simultaneously, formulate the underlying linear program and determine how long each plant need to be run in order to provide sufficient output and minimize the cost. (20 Marks)
QUESTION THREE – (20 MARKS)
A company has 3 supply points and three demand areas for a particular commodity. The cost of transporting 1 unit from a supply point to a demand area and the capacities are as given below:
Demand Areas Available 1 2 3
Supply
1 1 2 1 350 2 1 2 3 450 3 2 1 1 240 Required 360 480 300
3
By using minimum cost rule to make the initial allocation, obtain the optimal allocation that minimizes transportation cost. (20 Marks)
QUESTION FOUR – (20 MARKS)
In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed rabbits on a daily diet containing a minimum of 24g of fat, 36 g of carbohydrates and 4g of protein. But the rabbits should be fed no more than 5 ounces of food a day. Rather than order rabbit food that is custom-blended, it is cheaper to order food X and food Y and blend them for a optimal mix. Food X contains 8g of fat, 12g of carbohydrates and 2g of protein per ounce and costs $0.02 per ounce. Food Y contains 12g of fat, 12g of carbohydrates and 1g of protein per ounce, at a cost of $0.30 per ounce. Formulate the underlying linear programming problem and by finding the corresponding dual, obtain the minimum cost for the blend. (20 Marks)
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