Exercise 2 (Hint: The easiest model to enable you to answer the questions in this exercise is perhaps a network flow model; augmented for some questions by side constraints. However, any correct model is equally acceptable.) The production-planning data for an aggregate product are given in the Table below. Month January February March April May Capacity (units) 90 90 Demand (units) 30 50 150 50 85 Production Cost (S/unit) 2.1 3.2 1.5 2.75 120 100 115 2.7 10% of the production in any one month is defective and, therefore, cannot be used to satisfy demand. Units of the product can be stored in inventory. There will be 10 units in stock at the beginning of January and it is required to have a stock of 15 units at the end of May. It costs $0.2 per month to hold one unit in stock. 1. Build solve an Excel the optimal production plan, with the objective of minimizing total cost. Write down the optimal production plan and the optimal cost. [15 Points] 2. Copy the base model again to a new spreadsheet in your workbook and extend it to handle the following additional features (data are in the table below): There is a fixed charge for setting up production in any one month, as shown below. Month January February March Setup Cost ($) 50 60 70 Month Setup Cost ($) January 50 February 60 March 70 April 80 May 90 . If production is initiated, the number of units produced must be no less than 30. The objective is again to minimize the total cost. Solve the model and write down the production plan and the optimal cost. [15 Points]