INSTRUCTIONS: For the mathematical models either use Word Equations, or write down the formulas on a paper, take a photo you MUST upload the word file and an Excel Workbook. For the optimization problems, you must use the Excel solve

Question 1) (30 points) Consider a machine in a manufacturing center that can process multiple types of products. During a day, the machine is available for 3 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. Processing time 75 100 (minutes) m 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 dene 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: How long (in minutes) the machine remains idle during a clay? Answer: Idle time in minutes: What is the solution of the problem if we assume that we can sell multiple copies of each item? How the objective function value changes if we consider this new assumption? Use Excel to solve the problem with this new assumption. Answer: Value of the objective function with the new assumption