Question

Consider the following mathematical model minimize $x_1 + 3x_2 + f(x_3) + g(x_4)$ subject to the following constraints (a) Either $x_1 + 2x_2 + 3x_3 ge 6$ or $3x_2 + 4x_3 ge 9$. (b) At least two of the following four inequalities hold. $egin{cases} 5x_1 + 6x_3 + x_4 ge 9 \ 3x_1 + x_2 + 4x_3 le 10 \ x_2 + x_3 ge 1 \ 3x_3 ge 5 end{cases}$ (c) If $x_2 e 2$, then $x_1 ge 3$. (d) $x_4 = 0$ or 1 or 2. (e) $x_1, x_2$ and $x_3$ are integers. (f) $x_i ge 0, i = 1, 2, 3, 4$. where $f(x_3) = egin{cases} 8 + 3x_3 & ext{if } x_3 > 0; \ 3 & ext{otherwise,} end{cases}$ and $g(x_4) = x_4^2$. Formulate this as an integer programming problem.

          Consider the following mathematical model
minimize $x_1 + 3x_2 + f(x_3) + g(x_4)$
subject to the following constraints
(a) Either $x_1 + 2x_2 + 3x_3 ge 6$ or $3x_2 + 4x_3 ge 9$.
(b) At least two of the following four inequalities hold.
$egin{cases}
5x_1 + 6x_3 + x_4 ge 9 \
3x_1 + x_2 + 4x_3 le 10 \
x_2 + x_3 ge 1 \
3x_3 ge 5
end{cases}$
(c) If $x_2 
e 2$, then $x_1 ge 3$.
(d) $x_4 = 0$ or 1 or 2.
(e) $x_1, x_2$ and $x_3$ are integers.
(f) $x_i ge 0, i = 1, 2, 3, 4$.
where
$f(x_3) = egin{cases} 8 + 3x_3 & 	ext{if } x_3 > 0; \ 3 & 	ext{otherwise,} end{cases}$
and
$g(x_4) = x_4^2$.
Formulate this as an integer programming problem.

Consider the following mathematical model
minimize x1 + 3x2 + f(x3) + g(x4)
subject to the following constraints
(a) Either x1 + 2x2 + 3x3 ge 6 or 3x2 + 4x3 ge 9.
(b) At least two of the following four inequalities hold.
egincases
5x1 + 6x3 + x4 ge 9 3x1 + x2 + 4x3 le 10 x2 + x3 ge 1 3x3 ge 5
endcases
(c) If x2
e 2, then x1 ge 3.
(d) x4 = 0 or 1 or 2.
(e) x1, x2 and x3 are integers.
(f) xi ge 0, i = 1, 2, 3, 4.
where
f(x3) = egincases 8 + 3x3 extif x3 > 0; 3 extotherwise, endcases
and
g(x4) = x4^2.
Formulate this as an integer programming problem.

Added by Juana M.

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