following table:

$\backslash$table$[[$Item$,$Backpacks,Lunch boxes$],[$demand forecast,$30,000$ units$/$yr$,15,000$ units$/$yr$],[$lot size,$20$ units,$60$ units$],[$standard processing time,$0\mathrm{.}4$ hours$/$unit$,0\mathrm{.}5$ hours$/$unit$],[$standard setup time,$3$ hours$/$lot$,4$ hours$/$lot$]]$

The shop works two shifts per day, $8$ hours per shift, $180$ days per year. Currently, the company operates $5$ machines, and desires a $25$ percent capacity cushion. How many machines should be purchased to meet the upcoming year's demand without resorting to any short$-$term capacity solutions?