ALCCS
NOTE:
· Question 1 is compulsory and
carries 28 marks. Answer any FOUR questions from the rest. Marks are indicated against each question.
· Parts of a question should be
answered at the same place.
· All
calculations should be up to three places of decimals.
Q.1
a. Define Linear function and
linear inequalities. What do we understand by a linear programming problem?
b. List and explain the
assumptions of linear programming problem.
c. Relationship
between the primal problem and the dual problem.
d. Distinguish
between integer programming problem and linear programming problem. Give
examples?
e. Define
simulation and its advantages.
f. Discuss
the degeneracy in transportation problem.
g. Discuss the
complication arises due to unrestricted variables in a Linear Programming
problem. (7 4)
Q.2 a. Establish
the difference between
(i)
Feasible solution
(ii) Basic Feasible Solution
(iii)
Degenerate Basic Feasible Solution
(iv)
Optimum Basic Feasible Solution
(v) Explain the significance of shadow price. (9)
b. Discuss the components of a simplex tableau.
Obtain the dual problem of the following L.P.P.
Maximize
Subject
to the constraints
(9)
Q.3 a. Discuss transportation problem with suitable
examples. Also discuss the assignment
problem in brief.
(9)
b. A departmental head has four
subordinates, and four tasks to be performed. The subordinates differ in
efficiency, and tasks differ in their intrinsic difficulty. His estimate of the
time each man would take to perform each task is given in the matrix below: (9)
Men
Tasks
E F G H
A 18 26 17 11
B 13 28 14 26
C 38 19 18 15
D 19 26 24 10
How
should the tasks be allocated one to a man so as to minimize the total man
hours?
Q.4 a. What is revise simplex method? Discuss the advantages of Revised
Simplex Method over the ordinary simplex method. (9)
b. Use revised simplex method to solve the
L.P.P.,
maximize
subject
to the constraints
(9)
Q.5
Briefly, discuss the dynamic
programming problem. Define the principle of optimality of dynamic programming
approach and discuss the dynamic programming algorithm. (9)
Use
dynamic programming to solve the following L.P.P.
Maximize
subject
to
and
Q.6 Discuss the
various steps involved in simulation process.
Dr. Dilip is a dentist who schedules all his patients for 30
minutes appointments. Some of the patients take more or less than 30 minutes
depending on the type of dental work to be done. The following summary shows
the various categories of work, their probabilities and the time actually to
complete the work:
Category Time
Required Probability of
(minutes) category
Filling 45 0.40
Crown 60 0.15
Cleaning 15 0.15
Extraction 45 0.10
Checkup 15 0.20
Simulate the dentist’s clinic
for four hours and determine the average waiting time for the patients as well
as idleness of the doctor. Assume that all the patients show up at the clinic
at exactly their scheduled arrival time starting at 8:00 A.M. Use the following
random numbers handling the above problem.
40 82
11 34 25
66 17 79 (9)
Q.7 Write
short note on:
(i) Monte-Carlo Simulation Method
(ii) Properties of Gomery’s cutting plane method
and the steps involved to solve Integer Linear Programming Problem.
(iii)
Distinguish between simulation and modeling. (6+6+6)