Get premium membership and access revision papers, questions with answers as well as video lessons.

Operations Research Question Paper

Operations Research

Course:Bbit 323

Institution: Kenya Methodist University question papers

Exam Year:2008

KENYA METHODIST UNIVERSITY

END OF SECOND TRIMESTER 2008 EXAMINATIONS

FACULTY : BUSINESS AND MANAGEMENT STUDIES
DEPARTEMENT : BUSINESS ADMINISTRATION
COURSE CODE : BBIT 323
COURSE TITLE : OPERATIONS RESEARCH
TIME : 2 HOURS

INSTRUCTIONS:
• Answer Question ONE and any other TWO Questions

Question 1
(a) Define the following terms
(i) Operations research (2 marks)
(ii) Linear programming (2 marks)
(iii) An extreme point of a convex set (3 marks)
(iv) Optimal feasible solution (1 mark)
(v) Integer programming (2 marks)

(b) A firm manufactures headache pills in two sizes, A and B. Size A contains 2 grains of aspirin, 5 grains of bicarbonate and 1 grain of codeine; size B contains 1 grain of aspirin, 8 grains of bicarbonate and 6 grains of codeine. It has been found by users that it requires at least 12 grains of aspirin, 74 grains of bicarbonate and 24 grains of codeine for providing immediate effect. Determine the least number of pills a patient should take to get immediate relief. Also determine the quantity of codeine consumed by the patient.
(8 marks)
(c) Determine the dual of the following LP problem
Maximize
Subject to: (6 marks)
(d) Define a convex hull and show that given a set of points in , a convex hull is also a convex set. (6 marks)

Question 2
(a) State the duality theorem and the complementary slackness principle. Explain briefly their significance in operations research. (6 marks)

(b) Using simplex method solve the LP
Minimize
Subject to

(14 marks)

Question 3
A farmer has an initial capital of KES 230,000 and forty hectares of land on which he plants wheat, maize or beans. Each of the three crops requires KES 4,000, KES 6,000 and KES 6,000 respectively to cultivate. He also has 120 laborers and it requires 2 laborers per ha on wheat, 2 laborers per ha on maize and 4 laborers per ha on beans. The current market prices gives profit of KES 2,000, KES 2,500 and KES 2,800 per ha on wheat, maize and beans respectively. Assuming that the farmer intends to cultivate the whole land, formulate the underlying linear program and determine the number of hectares for each crop for maximum profit. (20 marks)

Question 4
(a) Outline the Gomory’s integer programming procedure (4 marks)
(b) Find the optimum integer solution to the following integer programming problem
Maximize
Subject to:

and integers (16 marks)

Question 5
(a) Obtain a dual program for the following primal
Maximize
Subject to

And (6 marks)
(b) Consider the linear programming problem
Minimize Subject to:

Unconstrained in sign
Put the above LP problem in canonical form (8 marks)

(c) With the aid of an example, discuss the economic interpretation of dual variables (6 marks)

Operations Research Question Paper

More Question Papers

Popular Exams