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Lecture 7.3 bt
 

Lecture 7.3 bt

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    Lecture 7.3 bt Lecture 7.3 bt Presentation Transcript

    • Today’s Agenda  Attendance / Announcements  Questions from Friday  Sections 7.3
    • Exam Schedule  Exam 4 (Ch 6,7) Fri 11/15  Exam 5 (Ch 10) Thur 12/5  Final Exam (All) Thur 12/12
    • 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
    • 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)
    • Linear Programming The Constraints are the inequalities that provide us with the Feasible Region.
    • Applications of Linear Programming The only thing we need to do today is to translate the word problem into the constraints and objective function.
    • let goats x let pigs y
    • Constraints: x y 16
    • Constraints: x y 16 x 10
    • Constraints: x y 16 25x 75 y 900 x 10 25x 75 y 900 25 x 3y 36
    • Constraints: x y 16 x 10 x 3y 36 x 0 y 0 Are there other “natural” or assumed constraints?
    • Constraints: x y 16 x 10 x 3y 36 Objective: x 0 y 0 P( x, y) 14x 40 y
    • 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
    • We want the greatest storage capacity S ( x, y) 8x 12 y
    • Classwork / Homework • Page 409 • 1 – 11 odd