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DMORMidterm

# DMORMidterm - UF-ESI-6314 DMOR-Midterm Cover package page 1...

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UF-ESI-6314 DMOR-Midterm Cover page 1 of 1 package page -L of 36 Name: Luther Setzer ESI 6314: Midterm Take Home Exam Due November 3rd There are five total questions. Please remember that you are not allowed to communicate with anyone regarding this exam except for the instructor or the TAs. Mtrl/t Luther Setzer 1 NASA Pkwy EStop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435

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UF-ESI-6314 DMOR-Midterm-01.xls Problem Statement page 1 0f 6 . package page 2 of :if., ...:-\ @ Question 1 (15 points): True/False and why/why not The following five questions are true/false. Credit is given only if a brief rationale is provided with your answers. (A sentence or two will suffice.) A simple "true" or "false" will not earn any points. Luther Setzer 1 NASA Pkwy EStop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435
UF-ESI-6314 DMOR-Midterm-01.xls Part A Part A (3 points): All optimal solutions to a linear program exist at extreme points. page 2 0f 6 package page "3 0f ~ False. A set of optimal solutions can also exist along a line between two extreme points. See Homework 3 Question 3 Part G for an example. In that problem, the iterations led to an optimal solution of z = Xl + X2 = 8 along the line X2 = 8 - Xl so that a range of solutions existed from Xl = 8/3 to 4 and X2 = 4 to 16/3 along that line. // V/ Luther Setzer 1 NASA Pkwy EStop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435

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UF-ESI-6314 DMOR-Midterm-01.xls Part B page ;1of 6 package page ~of~ Part B (3 points): In the simplex method for a minimization problem, the objective function strictly decreases at each iteration until an optimal solution is found. (An iteration consists of entering a nonbasic variable and exiting a basic variable.) True. This Because the function at step brings Luther Setzer comes of necessity by the nature of the simplex method. method seeks to improve the performance of the objective each iteration, a failure to find improvement at a particular an end to the iterative process. UM. 6J D,~e(o 1 NASA Pkwy EStop NEM3, Kennedy Space Center, FL 32899 '7 ~ ;tt; (321) 544-7435
UF-ESI-6314 DMOR-Midterm-01.xls Part C page 4 of 6 - package page 5 of '% Part C (3 points): The minimum ratio test is designed to ensure that no variable becomes negative in our solution (except maybe for the z-value itself). True. According to Introduction to Mathematical Programming page 143: "The smallest ratio is the largest value of the entering variable that will keep all the current basic variables nonnegative." /// When working with a simplex tableau, performing this test becomes crucial to assure that no basic variable becomes negative on the path to the final solution. Luther Setzer 1 NASA Pkwy EStop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435

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UF-ESI-6314 DMOR-Midterm-01.xls Part D page ~ 0f 6 package page 12 of % Part D (3 points): If both a primal problem and its dual have feasible solutions, neither problem can be unbounded.
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DMORMidterm - UF-ESI-6314 DMOR-Midterm Cover package page 1...

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