Question $8$

$14$ pts

Trader Dan's needs a capacity plan for their critical operations in the upcoming years. Compared to their current operations, Trader Dan's is expecting to increase their sales ten$-$fold in the near future. Currently they produce three products: pierogi, borscht and kielbasi. Each of these products uses a common machine at Workstation F in their production process. Below is a table of relevant information for each product.

$\backslash$table$[[$Product$,\backslash$table$[[$Predicted$],[$Annual$],[$Demand$]],\backslash$table$[[$Processing$],[$Time$],[($seconds$)]],\backslash$table$[[$Set$-$up$],[$Time$],[($seconds$)]],$Lot size$],[$Pierogi$,38,434,360,85,346],[$Borscht$,36,008,180,157,309],[$Kielbasi$,86,193,180,106,415]]$

Trader Dan's operates one $8-$hour shift, $7$ days a week, $50$ weeks per year. Dan has determined a capacity cushion of $8\%$ is sufficient. How many machines does Dan need to have to meet the company's processing needs?