1. Today’s Agenda
 Attendance
/ Announcements
 Questions from Friday
 Sections 7.3

2. Exam Schedule
 Exam
4 (Ch 6,7)
Fri 11/15
 Exam 5 (Ch 10)
Thur 12/5
 Final Exam (All)
Thur 12/12

3. Applications of Linear
Programming
• Assign Variables
• Can use a table to organize given
information
• Write constraints as a system of
inequalities
• Find Objective function
• Optimize over the feasible region

4. Linear Programming
The Objective Function is
what we need to maximize or
minimize. For us, this will be a
function of 2 variables, f(x, y)

5. Linear Programming
The Constraints are the
inequalities that provide us with
the Feasible Region.

6. Applications of Linear
Programming
The only thing we need to do
today is to translate the word
problem into the constraints
and objective function.

8. let goats x
let pigs y

9. Constraints:
x y 16

10. Constraints:
x y 16
x 10

11. Constraints:
x y 16
25x 75 y 900
x 10
25x 75 y 900
25
x 3y 36

12. Constraints:
x y 16
x 10
x 3y 36
x 0
y 0
Are there other
“natural” or
assumed
constraints?

13. Constraints:
x y 16
x 10
x 3y 36
Objective:
x 0
y 0
P( x, y) 14x 40 y

17. Cost less than $560
40x 80 y 560
Floor space less than 72 feet
6 x 8 y 72
And can’t have negative cabinets
x 0, y
0

18. We want the greatest storage capacity
S ( x, y) 8x 12 y

26. Classwork / Homework
• Page 409
• 1 – 11 odd