3 5 Linear Programming Linear Programming Businesses use

3 -5: Linear Programming

Linear Programming Businesses use linear programming to find out how to maximize profit or minimize costs. Most have constraints on what they can use or buy.

http: //www. phschool. com/atschool/academy 123/english/academy 1 23_content/wl-book-demo/ph-514 s. html Follow along on your Guided Notes. INTRODUCTION VIDEO

Find the minimum and maximum value of the function f(x, y) = 3 x - 2 y. We are given the constraints: n y≥ 2 Graph y = 2, shade above n 1 ≤ x ≤ 5 Graph 1 = x =5, shade in between the lines n y≤x+3 Graph y = x + 3, shade below

Linear Programming Find the minimum and maximum values by graphing the inequalities and finding the vertices of the polygon formed. n Substitute the vertices into the function and find the largest and smallest values. n

1 ≤ x ≤ 5 8 7 6 5 4 3 y≤x+3 y≥ 2 2 1 1 2 3 4 5

Linear Programming n D 1 ≤ x ≤ 5 8 7 6 5 B 4 3 y≤x+3 C A 2 1 1 2 3 4 5 y≥ 2

Linear Programming f(x, y) = 3 x - 2 y n A: f(1, 2) = 3(1) - 2(2) = 3 - 4 = -1 n B: f(1, 4) = 3(1) - 2(4) = 3 - 8 = -5 n C: f(5, 2) = 3(5) - 2(2) = 15 - 4 = 11 n D: f(5, 8) = 3(5) - 2(8) = 15 - 16 = -1

Linear Programming f(1, 4) = -5 minimum n f(5, 2) = 11 maximum n

Find the minimum and maximum value of the function f(x, y) = 4 x + 3 y n

y ≥ 2 x -5 6 5 4 y ≥ -x + 2 B 3 2 A 1 1 2 C 3 4 5

Vertices f(x, y) = 4 x + 3 y n A: f(0, 2) = 4(0) + 3(2) = 6 n B: f(4, 3) = 4(4) + 3(3) = 25 n C: f( , - ) = 4( ) + 3(- ) = -1 =

Linear Programming f(0, 2) = 6 minimum n f(4, 3) = 25 maximum n