# Linear Programming Exploration

## 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.