In solving LP problem - minimize z - 6x - 10y- subject to x - 6- y - 2- 2x - y - 10- x - 0- y - 0- which constraints are reduntant-

After plotting the graph of: x≥ 6 y≥ 2 2x+y≥ 10 x,y≥0 We get, only one critical point of intersevtion, i.e., (6,2) ∴ z_min=6× 6+10× ...

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Types of Linear Programing Problems

In solving LP...

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In solving LP problem : minimize $z = 6 x + 10 y$ , subject to $x \geq 6, y \geq 2, 2 x + y \geq 10, x \geq 0, y \geq 0,$ which constraints are reduntant?

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Minimize and maximize Z = 5x + 10y subject to constraints are x + 2y $\leq$ 120, x + y $\geq$ 60, x - 2y $\geq$ 0 and x, y $\geq$ 0.

Z = 7 x + 10 y

4 x + 6 y \leq 240

6 x + 3 y \leq 240

x \geq 10

x \geq 0, 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

z = 5 x + 10 y

x + 2 y \leq 120

x + y \geq 60

x - 2 y \geq 0

x \geq 0, y \geq 0

x + 2 y \geq 10, x + y \geq 6, 3 x + y \geq 8, x \geq 0, y \geq 0. T o m i n i m i z e : z = 3 x + 5 y S u b j e c t t o t h e c o n s t r a i n t s x + 2 y \geq 10, x + y \geq 6, 3 x + y \geq 8, x \geq 0, y \geq 0

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