If you have an investment fund which has four options $x_1,x_2,x_3,x_4$
More should be invested in the combination of funds $x_2$ and $x_3$ than funds $x_1$ and $x_4$ by a ratio of at least $1.5:1$.
The constraint I have formed is as follows:
$$1.5(x_2 + x_3) - (x_1 + x_4) \geq 0.$$
Would this be the correct representation?
Thanks
No it is not right. The inequality should be
$\frac{1}{1.5}(x_2 + x_3) - (x_1 + x_4) \geq 0$
This is equivalent to
$\frac{2}{3}(x_2 + x_3) - (x_1 + x_4) \geq 0$
If $x_1 + x_4= 100$ the inequality holds if $x_2 + x_3\geq 150$
But there are two additional readings.
1) In $x_2 + x_3$ has be at least 1.5 time more invested than in $x_1 + x_4$
This means that $x_2 + x_3$ has to be (at least) $2.5(=1+1.5)$ times of $x_1 + x_4$
$\frac{1}{2.5}(x_2 + x_3) - (x_1 + x_4) \geq 0$
This is equivalent to
$0.4(x_2 + x_3) - (x_1 + x_4) \geq 0$
If $x_1 + x_4= 100$ the inequality holds if $x_2 + x_3\geq 250$
2. Interpreting of "more"
a) 1.5 is more than 1. Therfore it could be an equality sign.
$$\frac{2}{3}(x_2 + x_3) - (x_1 + x_4) = 0$$ or
$$0.4(x_2 + x_3) - (x_1 + x_4) = 0$$
b) The ratio has to be more than 1.5
$$\frac{2}{3}(x_2 + x_3) - (x_1 + x_4) \geq 0$$ or
$$0.4(x_2 + x_3) - (x_1 + x_4) \geq 0$$
For me the condition is not well defined and I have the 4 possible variants above.
