1. Linear Programming 1.3 M3

2. -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Warm-Up Graph the system.

3. -8-6-4 -2 2 42 68 4 6 -4 -6 -8 -2 8 Graph the system.

4. What is Linear Programming? 1. Way to maximize or minimize a linear objective function 2. Has constraint inequalities 3. Solutions (intersections) of the constraints are possible solutions to the objective function (equation)

5. General Example Concession Stand that Sells Hot Dogs & Hamburgers You have a certain amount of money to buy them. Only so many hot dogs will fit on the grill. (same with hamburgers) You want to know how much of each to buy to give you the Maximum Profit.

6. You Have 3 Unknowns Hot Dogs (x) Hamburgers (y) Maximum Profit (z) 2 unknowns are graphed on a coordinate plane. 3 unknowns will create a 3 dimensional graph. (x, y, z) x z y

7. To Solve 1. Graph the Inequalities 2. Identify the solutions (intersections) 3. Substitute the solutions into the objective function (equation) 4. Look for the answer to the problem. (maximum or minimum value)

8. Find the minimum value and the maximum value of the objective function C = 3x + 2y subject to the following constraints.

9. Understanding with Play-doh 1. Place you play-doh on top of your graph. 2. Trim the edges of your play- doh to be constraint equations. 3. The linear programming concept builds a 3D model that has its top base sliced at an angle. The highest vertex is at the maximum value and the lowest vertex is at the minimum value. 4. Identify the maximum vertex and slice the top base at an angle towards your minimum vertex.