UNIT 2: LINEAR PROGRAMMING



UNIT 2: LINEAR PROGRAMMING PROJECTPART I: Fund Raising and Linear Programming (25 points)Suppose that in order to raise money for homecoming your class needed a way to raise money. The student government decided that a sale fundraiser would be the best option. The student body decided to order cases of Hershey’s chocolate bars, and cases of jarred popcorn. However, the student body also decided that the class could order no more than 400 candy bars and jars of popcorn, and spend no more than $500. How can the class maximize their profit?Hershey’s chocolate bars come with 30 candy bars in a case.You pay: $10 per caseYou sell: $1.00 per candy barPopcorn comes with 10 jars in a case.You pay: $20 per caseYou sell: $5 per jarDEFINE:Let x represent the number of cases of Hershey’s chocolate bars ordered.Let y represent the number of cases of popcorn ordered.Let P represent the total profit.Hershey’s barsPopcornTotalNumber of casesNumber of unitsCostIncomeProfitWrite the restrictions. Then simplify them.Write the objective function.Graph the restrictions and label the vertices.Find the coordinates of each vertex.Evaluate P at each vertex.What is the maximum profit and when does it occur?Part II: Linear Programming and your business (60 points)Suppose that you are a local business owner and you have products that you want to sell. Your first step is to identify what type of business you want to own and then identify two products that you want to produce and sell. You will start you business with $10,000. For this project, ignore costs associated with keeping the business running, like rent, heat, electric, etc. Assume that all costs are already taken care of, and the $10,000 you have is just for producing your product. The only restriction you have in terms of spending the $10,000 is that you can not spend more than three quarters of it on the production of one of the products. Use linear programming to set up a profit model for your business. You will need to arbitrarily assign costs for the production of each product, and then determine how much you are going to sell your product for. You will then develop a profit model and set up a system of restrictions. You will need to graph those restrictions and then determine what you will need to sell in order to maximize your profit. You will want to set up a table to help you organize your data. Make sure that you clearly identify your profit model and restrictions. Your graph should be neatly constructed and properly labeled (ON GRAPH PAPER.) Make sure that you identify all critical points and then determine how you will reach maximum profit. *USE PART I AS A GUIDE*RUBRICLinear Programming Project (100 points)Part IThe table correctly represents the data given in the word problem.5 points_______The inequalities accurately represent the constraints given in the problem.4 points_______The objective function accurately represents the profit constraints.1 point_______The graph correctly shows the restrictions and feasible region.5 points_______The coordinates of the vertices are correct.4 points_______The profit is evaluated based on the objective function for each vertex.4 points_______The maximum profit is identified and when it occurs.2 points_______Total_______/25Part IIA business is identified and described. Costs and prices are given fortwo identified products.5 points_______A profit model is appropriately identified (possibly using a table similarto Part I).5 point _______The inequalities accurately represent the constraints given in the problem.4 points_______An objective function accurately represents the profit constraints.1 point_______The graph correctly shows the restrictions and feasible region.5 points_______The coordinates of the vertices are correct.4 points_______The profit is evaluated based on the objective function for each vertex.4 points_______The maximum profit is identified and when it occurs.2 points_______Total_______/30TOTAL SCORE _______/55 ................
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