# Linear Programming Exploration

- Author:
- Rose Neal, Tim Brzezinski

## This applet provides a modifiable template that allows you to graph up to a maximum of 4 linear inequalities (constraints c, d, e, and f).

When graphing solution sets to systems of linear inequalities, it is automatically assumed (by default) that both

*x*and*y*are greater than or equal to zero (see constraints*a*and*b*).**Begin by clicking OFF each of the buttons.**1. Click on each constraint one at a time. What do you NOTICE? 2. Click on the SHOW buttons, one at a time. What do you NOTICE? 3. What are the maximum and minimum values?**The feasible region will be shaded in pink.**What does this region represent?**Try another example.**1. Change each of the following constraints as indicated below. Type it in as you see below. The program will change it. c : 2x + 3y >= 12 d : 7x + 4y >= 28 e : y <=6 f : x <= 5 What do you notice? How is this the same as the first example? What are the minimum and maximum values?**Additional feature:**You can use the**INTERSECT**tool to determine the point (*x*,*y*) at which any two boundary lines intersect.