For the constraints aligned 3x+4y & 24

MATHEMATICS · Multi-part · CBSE · Mathematics · Linear Programming · Linear Programming

Problem

For the constraints 3x+4y≤24,x+y≥5,x≥0,y≥0,\begin{aligned} 3x+4y &\le 24,\\ x+y &\ge 5,\\ x &\ge 0,\\ y &\ge 0, \end{aligned} examine the four points A(2,6)A(2,6), B(4,2)B(4,2), C(3,3)C(3,3) and D(6,1)D(6,1). (i) Determine, with complete justification, which of the given points lie in the feasible region. (ii) For every point that lies on the boundary of the feasible region, identify the specific boundary line involved.

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