Answer to Question #200055 in Linear Algebra for kgomotso

Question #200055
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
1
Expert's answer
2021-05-31T06:55:52-0400

Solution:

Given,

"y\\ge5-2.5x;\n\\\\y\\le3-x;\n\\\\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).}\n\\\\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.


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