Spring 2010 Exam 1 Solutions

Spring 2010 Exam 1 Solutions - STOR 112 Spring 2010 Exam 1...

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Unformatted text preview: STOR 112 Spring 2010 Exam 1 Solution 2010-2-25 Instructions: • The exam consists of 6 questions for a total of 120 points. • Work the problems in a blue book. You can write on the exam, but it will not be graded. • Make sure your name and section number are on your blue book. (Section 1 = Pataki; Section 2 = Anderson). • Clearly mark each problem number. Please answer the problems in order. Start each problem on a new page.(If you want to skip a problem, leave plenty of space for that problem). • You may use a calculator. • For LP and IP formulations, you must give a clear definition of the decision variables, an objective function, and the constraints. Give a descriptive label for the objective AND each constraint(such as ”profit”). • Do not make assumptions about the solution based on the problem data (such as, product A makes much less profit than product B, so we will not make any of it, and exclude it from the formulation), even if it is possible to do so. • Write all constraints in the standard form: variables on the left side and a number on the right. • When turning in your exam, please show your UNC OneCard to one of the in- structors. Please return the exam paper as well. Question 1. (10 points) Consider the linear programming problem max 10 x 1 + 3 x 2 st.- x 1- x 2 ≤ - 6 (1) 3 x 1- 2 x 2 ≤ 3 (2)- 2 x 1 + 3 x 2 ≤ 13 (3) x 1 ,x 2 ≥ . • Graph the feasible region. • List all the corner points, and show how to find their coordinates. List the objective value of the corner points. • What is the optimal value of the LP? 1 Solution. • Graph the feasible region. • List all the corner points, and show how to find their coordinates. List the objective value of the corner points. Corner point A: at the meeting of constraints (1) and (2). We need to solve- x 1- x 2 =- 6 3 x 1- 2 x 2 = 3 to get A = (3 , 3) . Objective value is 39. Corner point B: at the meeting of constraints (1) and (3). We need to solve- x 1- x 2 =- 6- 2 x 1 + 3 x 2 = 13 to get B = (1 , 5). Objective value is 25. Corner point C: at the meeting of constraints (2) and (3). We need to solve 3 x 1- 2 x 2 = 3- 2 x 1 + 3 x 2 = 13 to get C = (7 , 9). Objective value is 97. 2 • What is the optimal value of the LP? It is 97, attained at the point C. Question 2. (15 points) A farmer has 10 acres to plant in wheat and corn. He has to plant at least 3 acres of wheat. Moreover, the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of corn. The profit is $300 per acre of wheat and $500 per acre of corn. Formulate a linear programming problem to find out how many acres of each should be planted to maximize total profit....
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This note was uploaded on 11/27/2011 for the course STOR 112 taught by Professor Rubin,david during the Fall '06 term at UNC.

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Spring 2010 Exam 1 Solutions - STOR 112 Spring 2010 Exam 1...

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