3.2 Linear Programming 3 Credits AS 91574

Optimization - Finding the minimum or maximum value of some quantity. Linear programming is a form of optimization where you optimize an objective function with a system of linear inequalities called constraints. The overlapped shaded region is called the feasible region.

Solving a linear programming problem Graph the constraints. Locate the ordered pairs of the vertices of the feasible region. If the feasible region is bounded (or closed), it will have a minimum & a maximum. If the region is unbounded (or open), it will have only one (a minimum OR a maximum). 4. Plug the vertices into the linear equation (C=) to find the min. and/or max.

A note about: Unbounded Feasible Regions If the region is unbounded, but has a top on it, there will be a maximum only. If the region is unbounded, but has a bottom, there will be a minimum only.

Find the min. & max. values of C=-x+3y subject to the following constraints. Vertices of feasible region: (2,8) C= -2+3(8)= 22 (2,0) C= -2+3(0)= -2 (5,0) C= -5+3(0)= -5 (5,2) C= -5+3(2)= 1 x  2 x  5 y  0 y  -2x+12 Max. of 22 at (2,8) Min. of -5 at (5,0)

Ex: C=x+5y Find the max. & min. subject to the following constraints y2x+2 5x+y Vertices? (0,2) C=0+5(2)=10 (1,4) C=1+5(4)=21 Maximum only! Max of 21 at (1,4)

what you need to know how to plot linear equations how to plot linear inequalities how to put multiple inequalities on a graph and shade it in how to read the maximum and minimum off the graph solve problems based on your skills