$15$ a$)$ Let us consider an equipment that functions using four components connected in series. Each component has certain reliability and the reliability of the equipment is the product of the individual reliabilities. In order to increase the reliability of the equipment, we can have some additional component in standby. The reliabilities and cost for standby units for the four components are shown in the following table.

$\backslash$table$[[\backslash$table$[[$Number$],[$of units$]],$Component A$,$Component B$,$Component C$,$Component D$,],[$Reliability$,$Cost,Reliability,Cost,Reliability,Cost,Reliability,Cost$],[1,0\mathrm{.}6,6,0\mathrm{.}4,10,0\mathrm{.}7,5,0\mathrm{.}5,8],[2,0\mathrm{.}75,11,0\mathrm{.}65,14,0\mathrm{.}9,10,0\mathrm{.}6,13],[3,0\mathrm{.}85,15,0\mathrm{.}8,17,0\mathrm{.}95,14,0\mathrm{.}8,16]]$

We assume that Rs$.40$ is available. How many units of each component $($ including the standby$)$ should we have that maximizes the total reliability of the system?