Q. 19

Solve the given inequalities x + 2y ≤ 100, 2x + y ≤ 120, x + y ≤ 70, x ≥ 0, y ≥ 0 graphically in two – dimensional plane.

Answer :

The graphical representation of


is given by common region in the figure below.


.…… (1)


……. (2)


……. (3)


……. (4)


……. (5)


Inequality (1) represents the region below line (including the line ).


Inequality (2) represents the region below line (including the line ).


Inequality (3) represents the region in front of line (including the line ).


Inequality (4) represents the region above line (including the line ).


Inequality (5) represents the region below line (including the line )


Therefore,every point in the common shaded region including the points on the respective lines represents the solution for the given inequalities.


This can be represented as follows,



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