Question $4$: $[6$ points$].$ An electronic device consists of three components The three components are in series so that the failure of one component causes the failure of the device. The reliability $($probability of no failure$)$ of the device can be improved by installing up to three units in each component. The table listed below charts the reliability, $r,$ and the cost, c$.$ The total capital available for the construction of the device is $$10,000$

$\backslash$table$[[\backslash$table$[[$Number of$],[$parallel units$]],$Component $1,$Component $2,$Component $3],[r_1,c_1($$$),r_2,c_2($$$),r_3,c_3($$$)$