MIT15_053S13_lec10

It turns out that timing does not matter in this game

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Unformatted text preview: es. It turns out that timing does not matter in this game. All that matters is what square are clicked on. 2. Write the objective. 3. Write the constraints. If it is easier to express it using non-linear constraints, or logical constraints, then do this first. 32 Optimizing the game of fiver. 1 1 2 3 4 5 Let x(i,j) = 1 if I click on the square in row i and column j. x(i,j) = 0 otherwise. 2 3 4 5 33 Let’s write the formulation x(i,j) = 1 if I click on the square in row i and column j. x(i,j) = 0 otherwise. 34 Optimizing the game of fiver Minimize i,j=1 to 5 x(i, j) s.t. x(i, j) + x(i, j-1) + x(i, j+1) + x(i-1, j) + x(i+1, j) is odd for all i, j = 1 to 5. x(i, j) is 0 or 1 for all i, j = 1 to 5. x(i, j) = 0 otherwise. This (with a little modification) is an integer program. 35 Optimizing the game of fiver Minimize i,j=1 to 5 x(i, j) s.t. x(i, j) + x(i, j-1) + x(i, j+1) + x(i-1, j) + x(i+1, j) - 2 y(i, j) = 1 for all i, j = 1 to 5. x(i, j) is 0 or 1 for all i, j = 1 to 5. x(i, j) = 0 otherwise 0 ≤ y(i, j) ≤ 2; y(i, j) integer for i, j = 1 to 5. This is an integer program. x is odd if there is an integer y such that x – 2y = 1. 36 Should I give away the solution? 37 Trading for Profit Nooz is a contestant on Trading for Profits. Its main slogan is “I Trading for Profit” Nooz has just won 14 IHTFP points. We now join the quiz show to see what the 14 points are worth. 38 iPad 5 points Data server 7 points MIT ‘Brass Rat’ ring 4 points $500 gift certificate to Au Bon Pain Tutoring in 6.041 Probabilistic Systems Analysis Dinner with Prof. Orlin and the 15.053 TAs 3 points 4 points 6 points 39 iPad Data server 5 points 7 points 16 utils 22 utils Tutoring in 6.041 Probabilistic Systems Analysis Dinner with Prof. Orlin and the 15.053 TAs 4 points 6 points 11 utils MIT ‘Brass Rat’ ring 4 points 12 utils $500 gift certificate to Au Bon Pain 3 points 8 utils Nooz determines what each prize is worth to him. He measure everything in “utils” on a scale from 1 to 25. 19 utils 40 Prize iPad server Brass Rat 1 2 3 4 5 6 Points 5 7 4 3 4 6 Utility 16 22 12 8 11 19 Au Bon Pain 6.041 tutoring 15.053 dinner Budget: 14 IHTFP points. Write N...
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