# Unit 05: Linear Inequalities and Linear Programming

Here is the list of important questions.

- Graph the solution region of $2x+y \geq 2$ —
*BSIC Gujranwala (2016)* - Graph the feasible region subject to the following constraint: —
*BSIC Gujranwala (2016)*

$2x-3y \leq 6$

$2x+3y \leq 12$

$x \geq 0$, $y \geq 0$

- Graph the inequalities

$2x+y\geq 2$

$x+2y\leq10$

$x\geq0,y\geq0$ —*BSIC Gujranwala (2015)* - Indicate solution set of linear inequality $2x+3y\leq 12$ by shading. —
*BSIC Gujranwala (2015)* - Maximize $z=x+3y$

Subject to

$2x+5y\leq30$

$5x+4y\leq20$

$x\geq0$, $y\geq0$ —*BSIC Gujranwala (2015)* - Graph the feasible region of the system of linear inequalities

$x+2y\leq 14$

$3x+4y\leq 36$

$2x+y\leq 10$

$x\geq0, y\geq0$ and find the corner points. —*FBSIC (2017)* - Maximize $f(x)=2x+5y$ subject to the constraints

$-x\leq8$

$-y\leq4$

$x\geq0, y\geq 0$ .—*FBSIC (2016)* - Find the area bounded $\cos x$ function from $x=-\frac{\pi}{2}$ to $x=\frac{\pi}{2}$.—
*BSIC Rawalpindi (2017)* - Graph the solution set of the linear inequality $x+y \geq 5$ by shading.—
*BSIC Rawalpindi (2017)* - Minimize $z=3x+y$ subject to the constraints

$3x+5y\geq 15$

$x+6y\geq 9$

$x\geq0, y\geq0$ —*BSIC Rawalpindi (2017)* - Graph the feasible region of following inequality $2x-3y\leq6$ —
*BSIC Sargodha(2016)* - Graph the feasible region of following system of linear inequalities, also find corner points $2x-3y\leq6\\ 2x+3y\leq 12\\ x\geq0, y\geq 0$—
*BSIC Sargodha(2016)* - Define feasible region and feasible solution.—
*BSIC Sargodha(2017)* - Define optimal solution.—
*BSIC Sargodha(2017)* - Graph the feasible region of the following system of linear inequalities, also find corner points

$2x+3y \leq 18$

$2x+y\leq 10$

$x+4y\leq 12$

$x\geq0, y\geq 0$.—*BSIC Sargodha(2017)*