You have been asked to put together a capacity plan for a critical operation at the Surefoot Sandal Company. Your capacity measure is number of machines. Thiree products $($men$\text{'}$s$,$ women's, and children's sandals$)$ are manufactured. The time standards $($processing and setup$),$ lot sizes, and demand forecasts are given in the following table. The firm operates two $8-$hour shifts, $5$ days per week, $50$ weeks per year. Experience shows that a capacity cushion of $5$ percent is sufficient.

$\backslash$table$[[$Product$,$Time Standards,,,$],[$Men$\text{'}$s sandals,$\backslash$table$[[$Processing$],[($hr$/$pair$)]],\backslash$table$[[$Setup$],[($hr$/$lot$)]],\backslash$table$[[$Lot size$],[($pairs$/$lot$)]],\backslash$table$[[$Demand Forecast$],[($pairs$/$yr$)]]],[$Women$\text{'}$s sandals,$0\mathrm{.}05,0\mathrm{.}5,240,80,000],[$Children$\text{'}$s sandals,$0\mathrm{.}10,2\mathrm{.}2,180,60,000],[$M$,0\mathrm{.}02,3\mathrm{.}8,360,120,000]]$

a$.$ How many machines are needed?

b$.$ If the operation currently has two machines, what is the capacity gap?