week1_handout-1

She can make cookies or brownies one batch of cookies

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Unformatted text preview: vings as possible. She can make cookies or brownies. One batch of cookies requires 1 cup of flour, 1/2 cup of butter and 3/4 cup of sugar. One batch yields 24 servings of cookies. ￿ She can also make brownies. One batch of brownies requires 1/2 cup of flour, 1 cup of butter, 2 cups of sugar, and 1 cup of cocoa. One batch yields 32 servings of brownies. ￿ Allie’s baking supplies include 4.5 cups of flour, 3 cups of butter, 6 cups of sugar, and 2 cups of cocoa. How many batches of cookies and brownies should she make? 6 / 19 Example: Formulate an LP Sugar Cookies vs. Brownies maximize subject to 24c + 32b c + .5b ≤ 4.5 .5c + b ≤ 3 .75c + 2b ≤ 6 b≤2 c≥0 b≥0 Flour Butter Sugar Cocoa What does this look like? 7 / 19 Example: Graphical Method for Solving LP Just the constraints: blue = flour, green = butter, red = sugar, black = cocoa What is the feasible region? What are the extreme points? 8 / 19 Example: Graphical Method for Solving LP Showing the objective function: How would you find the optimal solution? 9 / 19 Example: Graphical Method for Solving LP Optimal Solution: 10 / 19 Tricks for Converting to LPs ￿ Minimax Objective Functions ￿ Absolute Value 11 / 19 Tricks for LPs - Minimax Object...
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This note was uploaded on 12/10/2013 for the course MS&E 211 taught by Professor Yinyuye during the Fall '07 term at Stanford.

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