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Lecture 7.3 bt

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Lecture 7.3 bt

1. 1. Today’s Agenda  Attendance / Announcements  Questions from Friday  Sections 7.3
2. 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. 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. 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. 5. Linear Programming The Constraints are the inequalities that provide us with the Feasible Region.
6. 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.
7. 7. let goats x let pigs y
8. 8. Constraints: x y 16
9. 9. Constraints: x y 16 x 10
10. 10. Constraints: x y 16 25x 75 y 900 x 10 25x 75 y 900 25 x 3y 36
11. 11. Constraints: x y 16 x 10 x 3y 36 x 0 y 0 Are there other “natural” or assumed constraints?
12. 12. Constraints: x y 16 x 10 x 3y 36 Objective: x 0 y 0 P( x, y) 14x 40 y
13. 13. 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
14. 14. We want the greatest storage capacity S ( x, y) 8x 12 y
15. 15. Classwork / Homework • Page 409 • 1 – 11 odd
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