$($b$)(10$ pts$.)$ The grocery store has introduced a pilot packaging service for customer pick$-$up$.$

For the program, the store employs one worker to prepare the customers package. The

computer system estimates how much time is required to prepare each order. The customer

may specify a desired due date for package pickup. If the store can ensure the due date,

then the customer is charged $$6.$ If the order is ready after the customers due date, the

customer is charged $$4.$ The data below shows $6$ customer orders with processing time in

minutes and customer due date in minutes elapsed from the store opening time.

$($i$)(7$ pts$.)$ Please find the sequence of orders to maximize packaging service revenue.

Please also specify the algorithm you use.

$($ii$)(3$ pts$.)$ The store from the example above decided to modify their process. They

decided to remove the desired due date input and charge a flat $$5$ dollar packaging

fee, but instead they would like to minimize the average wait time for the order

$($from the store opening time$).$ Please find the optimal sequence of orders. Please

also specify the sequencing method you use.