Solve the quadratic programming problem beales method

499

MA/MSCMT-10
December - Examination 2016
M.A./M.Sc. (Final) Mathematics Examination Mathematical Programming
Paper - MA/MSCMT-10

		[ Max. Marks :- 80

Section - A 8 × 2 = 16 Very Short Answer Questions
Note: Section ‘A’ contain 08 Very Short Answer Type Questions.

Examinees have to attempt all questions. Each question is of 02 marks and maximum word limit may be thirty words.

x = (x1 , x2........ xn)	g x j ( )	$	0	( j	=	1, 2.....

	(1)	(P.T.O.)

(vi) Write the dual of quadratic programming problem.

max f x ( ) = C X
T

(viii)Explain Bellman’s principle of optimality.

Note:	Section - B	4 × 8 = 32
Note:

strictly convex.

3) Solve the following L.P.P. with the help of revised simplex

-x 1 + 3x 2# 6

x , 1 x 2$ 0

min z				4 x 1
s t . .	5 x 1		+	3 x 2$
x 1#
x 2#				6
x , 1		x 2$		0	and are integers.
						(2)	(Contd.)

min.	z	=			4 x 1 2				+		2 x			2	+	x	2	-
min.	z	=			4 x 1 2				+		2 x			2	+	x	3	-
s.t. x 1			+			x 2			+		x 3		=		15
2 x 1				+			x 2			+		2 x 3			=	30
x 1			,	x 2				,

min ( ) = x 1 2 + x 2 2 + x 3 2

s.t. 4 x 1 + x 2 2 + 2 x 3 = 14

s.t. AX $b

where A is an mxn real matrix and G is an nxn real positive

x 2# 6

3 x 1 + 2 x 2# 18

min. x 1 2			+	x		2	+	x	2	i
min. x 1 2			+	x		2	+	x	3	i
s.t.	x 1	.	x 2	.	x 3$			5 0
x 1		,	x 2		,
MA/MSCMT-10 / 1000 / 4											(3)	(P.T.O.)

Examinees will have to answer any two (02) questions. Each

question is of 16 marks. Examinees have to delimit each

2 x 1 + 20 x 2 + 4 x 3# 15

6 x 1 + 20 x 2 + 4 x 3 = 20

	2 x 1		+		3 x 2	-	_	x 1 2	2	2
	2 x 1		+		3 x 2	-	_	x 1 2	2	3
s.t.	x 1	+		x 2#		1	6
	2 x 1		+	3 x 2#
	x , 1		x 2$			0

			=	x 1	+	x 2	-	x 1 2	+		-	2x
			=	x 1									2
s.t.	x , 1	x 2$		0									2

13) Find optimal solution of the convex separate programming

maxz	3 x 1
s.t.	4 x 1 2	+	x	2 2 #
x , 1					0
						(4)