# Second Year Math Linear Inequalities and Linear Programming

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2. Indicate the solution set of the following systems of linear inequalities by shading:\[\text { (iii) } \begin{array}{l}3 x+7 y \geq 21 \\x-y \leq 2\end{array}\]

2. Graph the feasible region of the following system of linear inequalities and find the corner points in each case.(i)\[\begin{array}{l}2 x+y \leq 10 \\x+4 y \leq 12 \\x+2 y \leq 10 \\x \geq 0 y \geq 0\end{array}\]

$1. Graph the solution set of each of the following linear inequality in x y -plane:(v) 2 x+1 \geq 0$

5. Graph the solution region of the following system of linear inequalities by shading.\[\text { (ii) } \begin{array}{l}3 x-4 y \leq 12 \\x+2 y \leq 6 \\x+y \geq 1\end{array}\]

2. Graph the feasible region of the following system of linear inequalities and find the corner points in each case.\[\text { (vi) } \begin{array}{l}2 x+y \leq 20 \\8 x+15 y \leq 120 \\x+y \leq 11 \\x \geq 0 y \geq 0\end{array}\]

Example 3. Graph the feasible regions subject to the following constraints.(a)\[\begin{array}{l}2 x-3 y \leq 6 \\2 x+y \geq 2 \\x \geq 0 y \geq 0\end{array}\]