MA/MSCMT-10
December Examination 2017
M.A./M.Sc. (Final) Mathematics Examination
Mathematical Programming
Paper MA/MSCMT-10
Time 3 Hours Max. Marks 80
Note: The question paper is divided into three sections B and C.
Section A 8 × 2 16
(Very Short Answer Type Questions)
Note: Section contain 08 very short Answer Type Questions. Examinees have to attempt all questions. Each question is of 02 marks and maximum word limit is thirty words.
Define Quadratic form.
What is Basic Feasible Solution.
Define constrained optimization problem and unconstrained optimization problem.
State the difference between all integer programming problem and mixed integer programming problem.
Define Convex programming problem.
State Bellman's principle of Optimality.
499
MA/MSCMT-10 1200 3 (P.T.O.)
499
MA/ MSCMT-10 1200 3 (Contd.)
Define bounded variable problem.
(viii) Write quadratic form
x12 2x22 7x32 4x1x2 6x1x3 5x2x3in matrix form.
Section B 4 × 8 32
(Short Answer Type Questions)
Note: Section contain 08 short Answer Type Questions. Examinees
will have to answer any four question. Each question is of
08 marks. Examinees have to delimit each answer in maximum
200 words.
Show that x2 is a convex function.
Find the dimension of a rectangular parallelepiped with largest
volume whose sides are parallel to the coordinate planes, to be
inscribed in the ellipsoid a 1
x
b
y
c
z
2
2
2
2
2
2

Use Lagrange's multiplier method, solve the following nonlinear
programming problem:
Minimize f 2x122x22 2x32 24x1 8x2 12x3 10
subject to x1 x2 x3 x1, x2, x3 0
Use Kuhn Tucker condition solve the following nonlinear
programming problem:
Max f 8x x2 subject to x x x 0.
Explain Primal function and Dual function in nonlinear programming.
Give the steps involved in separable programming problem.
499
MA/ MSCMT-10 1200 3
Solve by Dynamic programming Max z 8x1 7x2 s.t.
2x1 x2 8 2x1 2x2 #15 x1, x2 0
Prove that the set of all optimum solutions (global maximum) of the
general convex programming problem is a convex set.
Section C 2 × 16 32
(Long Answer Type Questions)
Note: Section contain 04 Long Answer Type Questions. Examinees
will have to answer any two questions. Each question is of
16 marks. Examinees have to delimit each answer in maximum
500 words. Use of non-programmable scientific calculator is
allowed in this paper.
10) Solve the following Ipp by standard form II revised simplex method:
Min z x1 2x2 2x1 5x2 6 x1 x2 2 x1 x2 0
11) Solve the following quadratic programming using wolfe's method:
Minimize f x2) x12 2x22 8x1 -10x2 s.t.
x1 x2 5 x1 2x2 8 x1, x2 0
12) Solve the integer programming problem: Max z 7x1 9x2 s.t.
-x1 3x2 6 7x1 x2 35 x1, x2 0 and x1 x2 are integers.
13) Solve the following Ipp by Branch and Bound technique Max
z x1 x2 s.t.
3x1 2x2 #12 x2 2 x1, x2 0 and x1 x2 are integers.