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)
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