Problem $3-4($Algo$)$

Penny$$s Pies is a small specialty supplier to a national coffee$-$house chain. Penny$$s makes three types of pies $($apple$,$ cherry, and pecan$).$ Penny$$s operates $250$ days per year with a single eight$-$hour shift. Capacity is controlled by the number of production lines within the bakery $($a line consists of mixing equipment, rolling and cutting equipment, an oven, and packaging equipment$).$

Pie Demand Forecast $($pies per year$)$ Processing Time $($minutes per pie$)$ Lot Size $($number of pies$)$ Setup Time $($minutes per setup$)$

Apple $175,5002\mathrm{.}345011\mathrm{.}2$

Cherry $98,6006\mathrm{.}358016\mathrm{.}8$

Pecan $43,4004\mathrm{.}714030\mathrm{.}3$

pictureClick here for the Excel Data File

Determine the number of production lines Penny$$s should have based on the information provided in the above table.

Note: Round up your answer to the next whole number.