Distribution has $20$ employees who are responsible for the activities, and all $20$ are trained to handle any of the three tasks. Each of these employees works $40$ hours per week for $50$ weeks. There is an allowance of $18$ percent of the employees$$ time for training and other administrative tasks. The total costs of distribution for the coming year are estimated to be $$885,600.$ When asked, the manager of Distribution estimated the following times for each of the three activities:

Taking orders: $8$ minutes.

Picking orders: $12$ minutes.

Packaging orders: $15$ minutes.

During the year, Distribution received $42,000$ orders. Because of out$-$of$-$stock events, pickers had to pick $49,000$ orders. $39,500$ orders were packaged.

Required: