Solve the following LPP graphically. Minimize\(Z=-3{ x }_{ 1 }+4{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }+2{ x }_{ 2 }\le 8\quad ,{ 3x }_{ 1 }+{ 2x }_{ 2 }\le 12\quad and\quad \quad { x }_{ 1 }\ge 0,{ x }_{ 2 }\ge 2.\)

Solve the following LPP graphically, Minimize \(Z=3{ x }_{ 1 }+5{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }+3{ x }_{ 2 }\ge 3,\quad { x }_{ 1 }+{ x }_{ 2 }\ge 2\quad and\quad { x }_{ 1 },{ x }_{ 2 }\ge 0.\)

Solve the following LPP graphically. Maximize \(Z={ x }_{ 1 }+{ x }_{ 2 }\)
Subject to the constraints \({ x }_{ 1 }-{ x }_{ 2 }\le -1,{ -x }_{ 1 }+{ x }_{ 2 }\le 0\quad and\quad { x }_{ 1 }+{ x }_{ 2 }\ge 0\)

Construct the network for the projects consisting of various activities and their precedence relationships are as given below:

Immediate Predecessor	A	B	C	D	E	F	G	H	I
Activity	B	C	D,E,F	G	I	H	J	K	L

Construct the network for the following:

Activity	A	B	C	D	E	F
Immediate Predecessor	-	-	-	A	B	C