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DMOR-03-04 - UF-ESI-6314 DMOR-03-04.xmcd page 1 of 7 03-04...

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UF-ESI-6314 DMOR-03-04.xmcd page 1 of 7 03-04. Optimize the following linear program by the simplex method. (That's the method given in Question 3, where you continue to enter and exit variables, until you cannot improve the objective function by increasing any nonbasic variable.) minimize: z 5 - x 1 x 2 + = subject to: x 1 - 3 x 2 + s 1 + 12 = x 1 x 2 + s 2 + 8 = x 1 0 s 1 0 x 2 0 s 2 0 Do not solve graphically or by Excel; it needs to be done by hand. (Of course, you may use either or both methods to verify that you got the right answer.) Start by letting s 1 and s 2 be basic variables (i.e. solve for z , s 1 , and s 2 in terms of x 1 and x 2 ). Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435
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UF-ESI-6314 DMOR-03-04.xmcd page 2 of 7 To visualize but not to solve the problem, graph the feasible region in the x 1 and x 2 dimensions. x 2_1 x 1 ( ) 1 3 12 x 1 + ( ) := x 2_2 x 1 ( ) 8 x 1 - := 0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10 x 2_1 x 1 ( ) x 2_2 x 1 ( ) x 1 x 1 , The area bounded above the x 1 axis, to the right of the x 2 axis, below the red line, and below the blue line represents the feasible region. Luther Setzer 1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899 (321) 544-7435
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UF-ESI-6314 DMOR-03-04.xmcd page 3 of 7 First rearrange the three equations to prepare them for simplex modeling including a revision to the objective function to standardize it into a maximization problem: maximize: z' 5 x 1 x 2 - = 1 z' 5 x 1 - 1 x 2 + 0 s 1 + 0 s 2 + 0 = (1) 0 z' 1 x 1 - 3 x 2 + 1 s 1 + 0 s 2 + 12 = (2) 0 z' 1 x 1 + 1 x 2 + 0 s 1 + 1 s 2 + 8 = (3) This system has m = 3 linear equations in n = 5 variables. Per the instructions of this problem, this requires setting x 1 and x 2 equal to zero and defining the remaining variables in those terms.
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