Pack'd is a producer of Backpacks and lunch boxes. Relevant data on the bottleneck operation in the shop for the upcoming fiscal year are given in the following 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?