3.5 Cont.

Warm-up (IN)

Learning Objective: to continue linear programming

xy

yx

82

452

1. Solve the system:

2. Graph the feasible region and list the coordinates of the vertices

0,0

162

12

205

yx

yx

xy

yx

No solution

(0,20)(2,10) (8,4) (16,0)

NotesEx 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 continue linear programming

c. List the coordinates of the feasible region.

(10,20), (60,20), (60,40), (10,90)

d. Write an objective function for the total profit from the sales of boards and jackets.

P b10 j12

Corner Point Principal -

Learning Objective: to continue linear programming

The max and min values of the objective function only occur at the vertices of the feasible region.

e. Find the profit at each vertex.

jbP 1210 (10,20) 20121010 P

340$P(60,20) 20126010 P

840$P

(10,90) 90121010 P1180$P

(60,40) 40126010 P1080$P

Max Profit!

10 boards and 90 jackets

Learning Objective: to continue linear programming

Ex 2 – Page 194 #37

2,2

2426 a.

yx

yx

b.

yxP 2050 c.

220$max

Learning Objective: to continue linear programming

Ex 3 – Page 192 #32

0,0

24

10846

a.

yx

yx

yx b.

yxP 3040 c.

780$max

HW – p. 193 #33-36

Out – explain the steps used to solve a linear programming problem.

Summary – I hope I can remember…

Test Wed!