Examine the system of inequalities aligned x+2y & 8, 2x+y & 14

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

Problem

Examine the system of inequalities x+2y≥8,2x+y≤14,x−y≤1,x≥0,y≥0.\begin{aligned} x+2y &\ge 8,\\ 2x+y &\le 14,\\ x-y &\le 1,\\ x &\ge 0,\\ y &\ge 0. \end{aligned} (i) Sketch accurately the feasible region determined by the above inequalities. (ii) Prove that the feasible region obtained in part (i) is a convex set. (iii) List the vertices of the feasible region in order of increasing xx–coordinate.

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