Minimize z - 6x - 2y- Subject to x - 2y - 3- x - 4y - 4 - 3x - y - 3 - x - 0- y - 0-

#10; #10; #10; Inequality #10; #10; #10; x+2y gt;=3 #10; #10; #10; x+4y gt;=4 #10; #10; #10; 3x+y gt;=3 #10 ...

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Law of Reciprocal

Minimize z ...

Question

Minimize $z = 6 x + 2 y,$ Subject to $x + 2 y \geq 3, x + 4 y \geq 4, 3 x + y \geq 3, x \geq 0, y \geq 0$ .

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Z = - 3 x + 4 y

x + 2 y \leq 8

3 x + 2 y \leq 12

x \geq 0

y \geq 0

Z = 6 x + 4 y

3 x + 2 y \geq 12

x + y \geq 5

0 \leq x \leq 5

0 \leq y \leq 6

Minimize Z = -3x + 4y, subject to constraints are $x + 2 y \leq 8, 3 x + 2 y \leq 12, x \geq 0 a n d y \geq 0$ .

Z = 3 x + 4 y

x + y \leq 4, x \geq 0, y \geq 0

Z = - 3 x + 4 y

x + 2 y \leq 8, 3 x + 2 y \leq 12, x \geq 0, y \geq 0

M a x i m u m Z = 4 x + y S u b j e c t t o x + y \leq 50 3 x + y \leq 90 x \geq 0, y \geq 0

M i n i m i z e Z = 200 x + 500 y S u b j e c t t o x + 2 y \geq 10 3 x + 4 y \leq 24 x \geq 0, y \geq 0

M a x, a n d M i n . Z = 3 x + 9 y S u b j e c t t o x + 3 y \leq 60 x + y \geq 10 x \leq y x \geq 0, y \geq 0

M i n i m i z e Z = 3 x + 2 y S u b j e c t t o x + y \geq 8 3 x + 5 y \leq 15 x \geq 0, y \geq 0

M i n i m i z e Z = x + 2 y S u b j e c t t o 2 x + y \geq 3 x + 2 y \geq 6 x \geq 0, y \geq 0

M i n . a n d M a x . Z = 5 x + 10 y S u b j e c t t o x + 2 y \leq 120 x + 2 y \geq 60 x - 2 y \geq 0 x \geq 0, y \geq 0

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Inequality	x+2y>=3	x+4y>=4	3x+y>=3	x>=0	y>=0
Corresponding equation	x+2y=3	x+4y=4	3x+y=3	x=0	y=0
Intersection of line with x-axis	(3,0)	(4,0)	(1,0)	-	-
Intersection of line with y-axis	(0,1.5)	(0,1)	(0,3)	-	-
Region	Non origin side	Non origin side	Non origin side	Origin side	Origin side