make a table consisting set, parameter, and decision variables. write the objective function, constraints and validation solutions with explanation.

A company currently has five different production centers and four different distribution centers. The company works off of a pull system, and so every month the distribution centers put in an order for how much product they will need, and the production centers will produce the product and send it to them. This demand MUST be met. It costs a lot of money to move the product so naturally the company wants to try and minimize the distance traveled as much as possible. The distance matrix between the production and distribution centers is provided below. A production center can send product to multiple distribution centers as needed, however each production center has only a certain capacity each month to produce product. Additionally, distribution centers can receive product from multiple production centers if required. 1. Formulate this problem as a linear model. Write out the equations of the objective function and all constraints. Remember to define your decision variables and parameters and explain what the objective function and each constraint is meant to do. 2. Represent this linear model on an Excel spreadsheet. 3. Using the Excel model, guess and test a valid solution (i.e., doesn't break any constraints). You do not need to find the optimal solution. 4. Interpret your solution. What is the total distance the product will need to travel? How much product is being sent from production center X to distribution center Y (list all non-zero X,X combinations)? 5. Consider a situation where the company doesn't want any of their production centers to sit idle. To prevent this, they make it a requirement that each production center produce and ship at least 5 units of goods each month, regardless of whether it will hurt the shipping distance or not. What additional constraint would you need to add to the model to enforce this new requirement? You do not need to remake the model in Excel again, just write out this new constraint set and explain how it works