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Unformatted text preview: Department of Industrial Engineering & Operations Research IEOR162 Linear Programming SAMPLE Midterm Exam 1 Fall 2011 Name: SAMPLE Midterm Exam 1 Grade: SAMPLE Midterm Exam 1 1. Consider the following linear program max 3 x 1- 2 x 2 s.t.- x 1- x 2 ≥ 5 (1) 2 x 1- x 2 ≤ 4 (2) x 2 ≤ 4 . (3) (a) Draw the constraints and then shade the feasible region. Draw an isoprofit line and then indicate the improving direction on your graph. Find an optimal solution x * = ( x * 1 ,x * 2 ), if any, or conclude that the problem is infeasible or unbounded. (b) Write down the binding constraints, if any, at the point ( x 1 ,x 2 ) = (2 , 0). (c) For the following alternative objective function min- 6 x 1 + 3 x 2 , determine whether the new linear program will be having a unique optimal solution, multiple optimal solutions, infeasible, or unbounded. 1 2. The Gotham City Police Department employs 30 police officers. Each officer works 5 days per week. The crime rate fluctuates with the day of the week, so the number of police officersper week....
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This note was uploaded on 10/24/2011 for the course IEOR 162 taught by Professor Zhang during the Fall '07 term at Berkeley.
- Fall '07
- Operations Research