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Unformatted text preview: UF-ESI-6314DMOR-03-04.xmcdpage 1 of 703-04.Optimize the following linear program by the simplex method. (That's the method given inQuestion 3, where you continue to enter and exit variables, until you cannot improve the objectivefunction by increasing any nonbasic variable.)minimize:z5-x1x2+=subject to:x1-3x2+s1+12=x1x2+s2+8=x1≥s1≥x2≥s2≥Do not solve graphically or by Excel; it needs to be done by hand. (Of course, you may use eitheror both methods to verify that you got the right answer.) Start by letting s1and s2be basicvariables (i.e. solve for z, s1, and s2in terms of x1and x2).Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435UF-ESI-6314DMOR-03-04.xmcdpage 2 of 7To visualize but not to solve the problem, graph the feasible region in the x1and x2dimensions.x2_1x1( )1312x1+( )⋅:=x2_2x1( )8x1-:=1234567891012345678910x2_1x1( )x2_2x1( )x1x1, The area bounded above the x1axis, to the right of the x2axis, below the red line, and below theblue line represents the feasible region.Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435UF-ESI-6314DMOR-03-04.xmcdpage 3 of 7First rearrange the three equations to prepare them for simplex modeling including a revision to theobjective function to standardize it into a maximization problem:maximize:z'5x1x2-=1z'⋅5x1⋅-1x2⋅+s1⋅+s2⋅+=(1)z'⋅1x1⋅-3x2⋅+1s1⋅+s2+12=(2)z'⋅1x1⋅+1x2⋅+s1⋅+1s2⋅+8=(3)This system has m= 3 linear equations in n= 5 variables. Per the instructions of this problem, thisrequires setting x1and x2equal to zero and defining the remaining variables in those terms.equal to zero and defining the remaining variables in those terms....
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This note was uploaded on 02/25/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Fall '09 term at University of Florida.

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