Finco has $$6,000$ to invest, and three investments are available. If dj dollars $($in thousands$)$

are invested in investment j$,$ then a net present value $($in thousands$)$ of rj$($dj$)$ is obtained,

where the rj$($dj$)$s are as follows:

r$1($d$1)=7$d$1+2($d$1>0)$

r$2($d$2)=3$d$2+7($d$2>0)$

r$3($d$3)=4$d$3+5($d$3>0)$

r$1(0)=$ r$2(0)=$ r$3(0)$

The amount placed in each investment must be an exact multiple of $$1,000.$ To maximize

the net present value obtained from the investments, how should Finco allocate the

$$6,000?$