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 tenfold 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$,35,394,360,118,270],[$Borscht$,33,506,180,161,338],[$Kielbasi$,86,732,180,116,350]]$

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?