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. 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. Use Excel solver to solve the optimization model. Answer: Notation and definition of the decision variables: Objective function: Constraints: 3- What is the solution of the problem if we assume that we can sell multiple copies of each item? 2- How long (in minutes) the machine remains idle during a day? How the objective function value changes if we consider this new assumption? Use Excel to solve the problem with this new assumption. Answer: Idle time in minutes: Answer: Value of the objective function with the new assumption