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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 nonlinear 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, j1) + x(i, j+1) + x(i1, 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, j1) + x(i, j+1) + x(i1, 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.
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 Spring '07
 JamesOrli
 Management, Alice in Wonderland

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