Download presentation

Presentation is loading. Please wait.

Published byTaylor Harrington Modified over 4 years ago

There are copies: 1

Do Now The cost of renting a pool at an aquatic center id either $30 an hr. or $20 an hr. with a $40 non refundable deposit. Use algebra to find for how.

1
Linear Programming

2
Businesses use linear programming to find out how to maximize profit or minimize costs. Most have constraints on what they can use or buy.

3
Find the minimum and maximum value of the function f(x, y) = 3x - 2y. We are given the constraints: y 2 1 x 5 y x + 3

4
Linear Programming Find the minimum and maximum values by graphing the inequalities and finding the vertices of the polygon formed. Substitute the vertices into the function and find the largest and smallest values.

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

6
Linear Programming The vertices of the quadrilateral formed are: (1, 2) (1, 4) (5, 2) (5, 8) Plug these points into the function f(x, y) = 3x - 2y

7
Linear Programming f(x, y) = 3x - 2y f(1, 2) = 3(1) - 2(2) = 3 - 4 = -1 f(1, 4) = 3(1) - 2(4) = 3 - 8 = -5 f(5, 2) = 3(5) - 2(2) = 15 - 4 = 11 f(5, 8) = 3(5) - 2(8) = 15 - 16 = -1

8
Linear Programming f(1, 4) = -5 minimum f(5, 2) = 11 maximum

9
Find the minimum and maximum value of the function f(x, y) = 4x + 3y We are given the constraints: y -x + 2 y x + 2 y 2x -5

10
6 4 2 5 34 5 1 1 2 3 y -x + 2 y 2x -5

11
Vertices f(x, y) = 4x + 3y f(0, 2) = 4(0) + 3(2) = 6 f(4, 3) = 4(4) + 3(3) = 25 f(, - ) = 4( ) + 3(- ) = -1 =

12
Linear Programming f(0, 2) = 6 minimum f(4, 3) = 25 maximum

Similar presentations

OK

3.3 Linear Programming. Vocabulary Constraints: linear inequalities; boundary lines Objective Function: Equation in standard form used to determine the.

3.3 Linear Programming. Vocabulary Constraints: linear inequalities; boundary lines Objective Function: Equation in standard form used to determine the.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google