(a) Define the term "non–negativity constraint" for a system of linear inequalities…

MATHEMATICS · Subjective · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

(a) Define the term "non–negativity constraint" for a system of linear inequalities in two variables. (b) For the system of inequalities x+2y≤10,y−3x≥−6,x≥0,y≥0,\begin{aligned} x+2y &\le 10,\\ y-3x &\ge -6,\\ x &\ge 0,\\ y &\ge 0, \end{aligned} explain, with reasons, why every point of the feasible region must lie inside the first quadrant of the coordinate plane. (c) If the inequality x≥0x\ge 0 is removed while the other three inequalities remain the same, describe qualitatively how the location and extent of the feasible region will change. State whether the first–quadrant limitation will still hold and justify your answer.

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