make a table consisting set, parameter and decision variable. write the objective function, constraints, and valid solutions with explanations

A company is trying to decide which of five different factories they should build to maximize profit from manufacturing and selling three different products. Each factory has an associated cost to build and will be able to produce any combination of each of the three products. However, due to local factors, the cost to produce a product at each factory will be different, and each factory will have a limited capacity of the total number of products of any kind that they can make (i.e., if the max capacity is 50, you can produce 20 of product 1,30 of product 2 , and 0 of product 3). Each product has its own market demand and sale price. Producing more of a product then there is demand for results in no additional profit. Additionally, not all demand needs to be met (i.e., if plant 2,3, and 4 made 75 of product 1 at a profit, but getting plant 1 to make the remaining 25 would yield a loss, they won't make those remaining 25 products). 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 expected profit for the company with your solution? Which factories are open? How many of each product does each factory make? Are you capturing all the demand