Application Project 2 Name: Date: For this project you will be building and solving our own linear program. In this scenario, you are starting a business and want to figure out how to make the most...

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Application Project 2 Name: Date: For this project you will be building and solving our own linear program. In this scenario, you are starting a business and want to figure out how to make the most money possible given a series of restric- tions that one might encounter in a real world situation. 1. Give a brief description of your company. (At least 2 sentences) List 2 products your company is looking to ship as well as how much money you make from each item. Include a picture of the product as with the price you found. It should look similar to this: 2. Express the following pieces of information as linear inequalities: (a) One store location needs to fill at least 10 slots on their shelves with your products. (b) Another store needs 2 of your first product and 8 of your second product in each slot, but only has at most 300 open slots on their shelves. (c) When manufacturing your product you have one machine which can make 2 of your first product and 4 of your second product every minute and has a total of 4 working hours each day. (d) You can only ship at most 50 of your second product each day. (e) You can only ship at most 100 of your first product each day. 3. If your objective if to maximum your revenue in a day, write out explicitly what your linear program will be based on your answers to parts 1 and 2. Make sure to explicitly state what is the objective function and what are the constraints. 4. Graph the feasible region of your linear program. Be sure to explicitly state what lines are associated with which constraint, clearly label your feasible region, and determine if it is bounded or unbounded. Please only shade in the feasible region. 5. Based on the feasible region you graphed in part 4, does your linear program indeed have an optimal solution? If so, explain why. 6. What are the corner points of your feasible region? List all of them, and label them in your graph from part 4. 1 7. Based on your answers to part 5 and 6, what is your optimal solution if it exists? Write out all of your work in determining the optimal solution. If one does not exist, express why. 8. Choose 2 new products that are different prices than the ones you found for part 1. What is your new objective function? Does your optimal solution change? Write out all of your work in determining the the optimal solution for this new objective function. 9. Write a brief summary of what you have learned during this assignment. Be sure to mention the differences in solutions between objective functions. (At least 4 sentences) 2