Part 3you MUST upload the word file and supporting Excel workbooks that are named by each question.

Question 3) (25 points) Consider a machine in a manufacturing center that can process multiple types of products. During a day, he machine is available for 8 hours. We have a set of potential tems 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 CDE F G Processing time 80 75 65 125 100 90 120 (minutes) Revenue (S) 529 990 748 805 575 727 773 1- Which items the manufacturer should select to process and sell to the customer in order to maximize his profit? Write a mathematical optimization model for this problem. Clearly define decision variables, objective function, and constraints for the optimization model. Use Excel to solve the optimization model. 2- How long (in minutes) the machine remains idle during a day? 3- What is the solution of the problem if we assume that we can sell multiple copies of each item? (Hint: this means, what happens if we consider integer values for decision variables instead of binary values when setting up the variable range constraints in Excel) How the objective function value changes if we consider this new assumption? Use excel to solve the problem with this new assumption