Show me the steps to solve This problem relates to tolerance stack$-$up using the absolute tolerance system, as explained in section $1-14.$ In the figure below, specified dimensions are as follows $($all units in inches$)$:

$\backslash$table$[[$a$,$b$,$c$,$d$],[1\mathrm{.}755+0\mathrm{.}002,9015+0004,3\mathrm{.}900+0007,?+0\mathrm{.}010]]$

$($a$)$ If the gap, $w,$ must be at least $0\mathrm{.}015$ in for the proper functioning of the assembly, what is the correct nominal dimension for $d?$

$($b$)$ Under the assumptions of the preceding question, what would be the most likely value for the gap, $w?$ Would it be $0\mathrm{.}015$ in $?$