Consider the system aligned y & x+4

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

Problem

Consider the system y≤x+4,y≥2x−3,y≤9−x,x≥0,y≥0.\begin{aligned} y &\le x+4,\\ y &\ge 2x-3,\\ y &\le 9-x,\\ x &\ge 0,\\ y &\ge 0. \end{aligned} (a) Draw the graphs of all five inequalities on the same set of axes and obtain the feasible region. (b) Determine, giving reasons, whether the feasible region is bounded or unbounded. (c) Verify algebraically whether the point (6,1)(6,1) belongs to the feasible region. (d) If the region is unbounded, describe the direction(s) in which it extends indefinitely; if it is bounded, give the coordinates of its extreme vertices.

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