Question $1)(25$ points$)$ Consider a machine in a manufacturing center that can process multiple types of products. During a day, the machine is available for $8$ hours. We have a set of potential items that can be processed on this machine and after the process, each item can be sold to a customer. Assume that we only can sell one copy of each item. Table below shows the processing times and the potential profit of each item.

Item A B C D E F

Processing time $($minutes$)7580958590100$

Revenue $($$$)432412754679545723$

$1-$ Which items the manufacturer should select to process and sell to the customer to maximize his profit? Write a mathematical optimization model for this problem. Clearly define decision variables, objective function, and constraints for the optimization model.

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