# What is linear programming?

### What is linear programming?

#### Lessons

Linear programming is the process of finding the optimized condition (the maxima and/or minima) of a function, given various linear inequalities as constraints.
• 1.
Finding Optimal Values Given Constraints In Slope-Intercept Form

Find the maximal and minimal value of $z=2x+3y$ subject to the following constraints:

$y \geq x+2$
$y \leq 3x$
$y \leq -2x+20$

• 2.
Finding Optimal Values Given Constraints In Standard Form

Given the following constraints, find the maximal and minimal value of $z=5x+6y$.

$x \geq 0$
$y \geq 0$
$x-6 \leq 0$
$-x+y \leq 6$
$x+y \leq 8$
$\frac{1}{2}x+y \geq 3$