Maximize Z $=0\mathrm{.}12$x$1+0\mathrm{.}07$x$2+0\mathrm{.}06$x$3$

Subject to the following constraints:

$1.$ Total investment amount: x$1+$x$2+$x$3<=15000$

$2.$ Investment in gold is twice the combined investment in the two top $100$ companies: x$3>=2($x$1+$x$2)$

$3.$ Investment of at least $7,000$ in gold and the established top $100$ medium risk company: x$2+$x$3>=7000$

$4.$ Investment of at least $6,000$ in the established top $100$ medium risk company and the new top $100$ high risk company: x$1+$x$2>=6000$

$5.$ Non$-$negativity constraint: x$1,$x$2,$x$3>=0$

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