(35pts) You are opening your own small boutique and need to decide the optimal product mix. There are three types of dresses you are considering: a purple dress which takes 8 hours to make and sells for $500, a red dress which takes 5 hours to make and sells for $200, and a green dress which takes 3 hours to make and sells for $100. Your team only has 450 hours of worktime before your store’s grand opening. Before making the dresses, you checked your inventory and found 125 bottles of red dye, 75 bottles of yellow dye, 150 bottles of blue dye, and 65 bags of sequins. The purple dress requires two bottles of red dye, one bottle of blue dye, and three bags of sequins to make. The red dress requires three bottles of red dye and one bag of sequins to make. The green dress requires two bottles of blue dye and one bottle of yellow dye to make (and no sequins). Since you don’t want too many purple dresses, you want the number of purple dresses to be less than or equal to both the red dresses and the green dresses combined. How many of each dress should you to maximize revenue? a) Formulate mathematically this LP model: state the decision variables, objective function, and list all the constraints. b) Solve the model using Excel Solver. Provide an image of your model, solver screen, and report the optimal solution. Round decimals to the nearest hundredth. c) Which constraint (if any) is non-binding?