EN.625.415 Midterm: Exam 1 Solutions Fall 2012
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Problem 1: (25 points) consider the following simplex tableau. All of the parts for problem 1 are short answer ; you do not need to show any computations at all. 2: write the associated basic feasible solution and its objective function value. Solution: one example is [. 01 2 3. 99 . 01 0 0 0]t , with objective function value 12. 02. Problem 2: (10 points) label each of the following statements true or false: suppose s rn, f : s r is continuously di erentiable, and x s is a boundary point of s. If x is a local minimizer of min f (x) s. t. x s, then f (x ) = ~0. False: a set s rn is closed if and only if each point of s c is an interior point of s c. true, if s rn is open then s is convex.
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1. The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
Minimize X1 + X2 + X3 + X4
Subject to: X1 + X4%u2265 12 (shift 1)
X1 + X2%u2265 15 (shift 2)
X2 + X3%u2265 16 (shift 3)
X3 + X4%u2265 14 (shift 4)
all variables %u2265 0
Find the optimal solution using QM.
How many workers would be assigned to shift 1? (Points : 3) 12
13
0
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| 10. ____________ is used to analyze changes in model parameters. (Points : 3) |
Feasible solution
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