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0-1 Knapsack optimization problem

Just consider the two cases: If $z_i=0$, the LHS and RHS are both $0$. If $z_i=1$, the LHS and RHS are both $p_i$. Explicit calculations for the RHS: \begin{align} \theta_i \left(1 - \left(\frac{\...
RobPratt's user avatar
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2 votes

Need help with integer programming exercise

As the problem only contains four variables let's define $f$ as the feasible solution space of the problem. Then $f$ contains $12$ feasible solutions: $\{(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1), (1,...
A.Omidi's user avatar
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1 vote

Need help with integer programming exercise

Given the system you presented $X = \{ x \in \{0, 1\}^4 : 97 x_1 + 32 x_2 + 25 x_3 + 20 x_4 \leqslant 139 \}$ (1) We have that, if $x_1 = 1$, then $x_2 + x_3 + x_4 \leqslant 1$, since any solution ...
Matheus Diógenes Andrade's user avatar
1 vote

Knapsack Problem with Multiple Properties

First, let $x_i=1$ if the $i$th example is picked, where $i \in \{1, 2, …, N\}$, and $x_i=0$ otherwise. If you want to maximize the sum of ALL the elements, simply a knapsack problem with non-varying ...
Mason's user avatar
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