3.5 Linear Programming

Warm-up (IN)

Learning Objective: to write and graph a set of constraints for a linear programming problem, then to find the maximum or minimum value of

an objective function.

82

7

yx

yx1. Solve the system:

2. Graph the solution:

1

0

5

32

y

x

xy

xy

(5, 2)

Linear Programming –

Notes

Ex 1 – Burton produces snowboards and jackets and sells them to stores. They will ship no more than 100 boards and jackets per day. The stores guarantee they will sell at least 10 and no more than 60 boards and at least 20 jackets per day. Burton makes a profit of $10 per board and $12 per jacket.

Learning Objective: to write and graph a set of constraints for a linear programming problem, then to find the maximum or minimum value of an objective function.

A method of finding a maximum or minimum value that satisfies all of the given conditions in a particular situation

a. Write a system of inequalities to represent the constraints. 0

100

10 60

20

b

b j

b

j

b. Graph the feasible region.

c. List the coordinates of vertices of the feasible region.

HW – p. 191 #10-17 p. 194 #38,39

Out – describe a real world situation in which the feasible region would be unbounded on the right.Summary – I understand…ORI’m confused about…

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