Question

what is the difference between bounded and unbounded feasible region in lpp maths class 12 th.. plzz dont copy from net.. not clear from there.. plzz ans from ur understanding.. plzz

Answer 1

We know that ,every point of the common region satisfied the both constraints including the non negativity restrictions is known as feasible region.

i)A feasible region is bounded if we can find a constant k such that the distance between any two points of region cannot exceed k .A region that is not bounded called unbounded.

ii) if the feasible region is unbounded then the optimal value of the objective function may or may not exist and if exist then it must be occur at one of the extreme point

example
i) z=3x+4y
subject to

4x+2y<=80
2x+5y<=180
x,y>=0
here origin satisfy in the equations.hence by drawing the graph we can find that the feasible region is bounded.
ii)z=20x+40y

subject to
2x+y>=8
x+4y>=4
x,y>=0
here we can find that origin doesn't satisfy both the equation.hence by drawing the graph we can find that the feasible region is unbounded.

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