• Create a new file for each of the following variations of problems studied in class. in each case, start with the original problem formulation, solve with integer (or binary) constraints on all of the decision variables, and set the integer optimality to 0 in the solver parameters > options dialog. please name your excel files as follows: • lastname-firstname-asmt5-prob1.xlsx • lastname-firstname-asmt5-prob2.xlsx • lastname-firstname-asmt5-prob3.xlsx email me your excel files by 9:00 am next tuesday, attaching all three to one email. send your message from your sfsu email account to avoid possibly being flagged as spam by the sfsu server. 
• 1. in the optimal solution to the original great threads manufacturing model, you’ll notice that no skirts are produced. suppose now that great threads has an order for 250 skirts that must be produced. modify the model as needed and have solver find the new optimal solution. 
• 1a) briefly explain why it is enough to just put a lower bound of 250 on the number of skirts produced, i.e., you need not also set skirt’s corresponding rent equipment variable to 1.
•  1b) how much profit does great threads lose by having to produce the skirts? 
• 2. in the optimal solution to the original great threads manufacturing model, only 2 products are produced: shorts and jackets. suppose now that great threads wants to produce at least 3 products, and the minimum production quantity for any product produced at a positive level is 100 items. modify the model as required and have solver find the new optimal solution. 
• 2a) how much profit does great threads lose by having to produce 3 products instead of 2?
•  2b) run a sensitivity analysis (either via solvertable or manually with solver, copying and pasting the results as needed) to see how sensitive the optimal solution and total profit are to the minimum production threshold when it varies from 50 to 300 in increments of 50. 
• 3. expand the western airlines hub location model to include 2 new cities: cleveland and dallas. you can obtain air (flight) mileage between the new and existing cities using the web site of your choice. use only whole numbers in your mileage data (e.g., 765, not 765.43). modify the model appropriately, assuming that the 2 new cities must be covered and are candidates for being hubs as well.
•  3a) what is the url of the web site you used to gather the mileage data? 
• 3b) what is the new optimal solution in terms of number of hubs? list the cities covered by each hub. 
• 3c) what’s the smallest coverage criterion (mile limit) for which 3 hubs cover all 14 cities?