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Show that the following system of linear inequalities has no solution x+2y\leq 3, 3x+4y\geq 12, x\geq 0, y\geq 1

Answers (1)

Given: x+2y\leq 3     Line: x + 2y = 3

x 3 1
y 0 1

Now, (0,0) doesn't satisfies 3x+4y\geq 12,

Thus, the region is not towards the origin

region is to the right of the y axis, thus,

x\geq 0

& Region is above the line x = 1, thus,

y\geq 1

Thus, the graph can be plotted as,

Therefore, the system has no common region as solution.

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