Question

consider the following set of inequalitis: y_>5-2.5x
y_<3-x
x,y_>0
the correct graphical representation of this set of inequalities is given by

Answer 1

Solution:

Given,

$y\ge5-2.5x; \\y\le3-x; \\x,y\ge0$

Plot $y=5-2.5x;\ y=3-x$ on graph.

Put $x=0,y=0$ in given inequations, we get,

$y\ge5-2.5x\Rightarrow 0\ge5\Rightarrow False\Rightarrow \text{Shaded portion/area under this inequality does not include O(0,0).} \\y\le3-x\Rightarrow 0\le3\Rightarrow True\Rightarrow \text{Shaded portion/area under this inequality includes O(0,0).}$

$x,y\ge0 \Rightarrow \text{Feasible region/area is in first quadrant only}$

This is required graphical representation of given inequalities and shaded region is the solution.