2.7 Linear Programming Objectives: Use linear programming procedures to solve applications. Recognize situations where exactly one solution to a linear programming application may not exist.

Linear Programming: Constraints: Linear Programming Procedure: Infeasible: Unbounded: Alternate optimal solutions: A procedure for finding the maximum and minimum value of a function in two variables subject to given constraints on the variables. Conditions given to variables, often expressed as linear inequalities. See page 112 (next slide) When the constraints of a linear programming problem cannot be satisfied simultaneously. The solution of a linear programming problem is unbounded if the region defined by the constraints is infinitely large. Where there are two or more optimal solutions.

Linear Programming Procedure: 1.) Define variables 2.) Write the constraints as a system of inequalities. 3.) Graph the system and find the coordinates of the vertices of the polygon formed. 4.) Write an expression whose value is to be maximized or minimized. 5.) Substitute values from the coordinates of the vertices into the expression. 6.) Select the greatest or least result.

Ex. 1) A manufacturer makes widgets and gadgets. At least 500 widgets and 700 gadgets are needed to meet minimum daily demands. The machinery can produce no more than 1200 widgets and 1400 gadgets per day. The combined number of widgets and gadgets that the packaging department can handle is 2300 per day. If the company sells both widgets and gadgets for $1.59 each, how many of each item should be produced in order to maximize profit? http://www.youtube.com/watch?v=2BZp2dxpwF8