DMOR-03-03

# DMOR-03-03 - UF-ESI-6314DMOR-03-03.xmcdpage 1 of...

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Unformatted text preview: UF-ESI-6314DMOR-03-03.xmcdpage 1 of 1003-03.Consider the following linear program:maximize:zx1x2+=subject to:x14x2+24≤2x1x2+12≤x1x2+8≤x1≥x2≥which we write in standard form as:maximize:zx1x2+=subject to:x14x2+s1+24=2x1x2+s2+12=x1x2+s3+8=x1≥x2≥s1≥s2≥s3≥Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435UF-ESI-6314DMOR-03-03.xmcdpage 2 of 10Part A:Graph the feasible region in the x1and x2dimensions.x2_1x1( )1424x1-( )⋅:=x2_2x1( )122x1-:=x2_3x1( )8x1-:=12345678910111213141516171819202122232425123456789101112131415x2_1x1( )x2_2x1( )x2_3x1( )x1x1, x1, The innermost area bounded between the x1axis, the x2axis, and the three colored lines representsthe feasible region.Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435UF-ESI-6314DMOR-03-03.xmcdpage 3 of 10Part B:At each extreme point, label the basic and nonbasic variables.This problem demands identifying the value of each of the five variables at each of the five extremepoints with all nonbasicvariables equaling zeroand the othersthus qualifying as basic.This five pointed polygon shape of the feasible region has five extreme points.One comes at the origin:x1=x2=s124=s212=s38=One comes at the intersection of the red line and x2axis:x1=x26=s1=s26=s32=One comes at the intersection of the blue line and x1axis:x16=x2=s118=s2=s32=One comes at the intersection of the red and green lines:8x1-1424x1-( )⋅=-->324x1⋅-24x1-=-->83x1⋅=x183=x2163=s1=s243=s3=One comes at the intersection of the blue and green lines:8x1-122x1-=x14=x24=s14=s2=s3=Luther Setzer1 NASA Pkwy E Stop NEM3, Kennedy Space Center, FL 32899(321) 544-7435UF-ESI-6314DMOR-03-03.xmcdpage 4 of 10Part C:Add the equationzx1-x2-=to the three constraints above. Suppose x1, s1, and s3are our basic variables. Use Gauss-Jordanelimination to solve for z, x1, s1, and s3in terms of the nonbasic variables x2and s2. (Note thatGauss-Jordan seeks to reduce the variables you're solving for into identity columns. If you'resolving for z, x1, s1, and s3, you already have three out of the four identity columns!)Based on the determinations in Part B, this part assumes a starting point at the intersection of theblue line and x1axis:x16=x2=s118=s2=s32=This problem presents four equations in four unknown basicvariables equaling four equations intwo unknown nonbasicvariables:1z1x1-s1+s3+x2=(1)z2x1+s1+s3+12x2-s2-=(2)z⋅1x1+1s1+s3+244x2-=(3)z1x1+s1+1s3⋅+8x2-=(4)Solving this problem requires creating a four row by four column matrix of coefficients of...
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DMOR-03-03 - UF-ESI-6314DMOR-03-03.xmcdpage 1 of...

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