LP Problem $\theta$ values and their corresponding number of iterations in brackets Optimal Solution Minimize $\begin{array}{l}Z=1.06{X}_{1}+0.56{X}_{2}+300{X}_{3}\\ \text{}+2703.50{X}_{4}+4368.23{X}_{5}\end{array}$ Subject to $1.06{X}_{1}+0.015{X}_{2}\ge 729824.87$ $0.56{X}_{2}+0.649{X}_{3}\ge 1522188.03$ $3.00{X}_{3}\ge 5040.16$ $2703.50{X}_{4}\ge 162210.06$ $4368.23{X}_{5}\ge 17472.92$ ${X}_{1},{X}_{2},{X}_{3},{X}_{4},{X}_{5}\ge 0$ 0.1 $\to$ (130) 0.3 $\to$ (42) 0.5 $\to$ (22) 0.7 $\to$ (15) 0.9 $\to$ (13) 0.2 $\to$ (62) 0.4 $\to$ (29) 0.6 $\to$ (16) 0.8 $\to$ (14) 1.0 $\to$ (5) $Z=2435620.485$ ${X}_{1}=688490.254$ ${X}_{2}=2716245.849$ ${X}_{3}=1680.053$ ${X}_{4}=60.000$ ${X}_{5}=4.000$ Minimize $\begin{array}{l}Z=2.03{X}_{1}+0.56{X}_{2}+2.93{X}_{3}\\ \text{}+1543.85{X}_{4}+1494.14{X}_{5}\end{array}$ Subject to $2.03{X}_{1}+0.015{X}_{3}\ge 3604.90$ $0.56{X}_{2}+\text{}0.633{X}_{3}\ge 430264.03$ $2.93{X}_{3}\ge 750.50$ $1543.85{X}_{4}\ge 26245.39$ $1494.14{X}_{5}\ge 5976.56$ ${X}_{1},{X}_{2},{X}_{3},{X}_{4},{X}_{5}\ge 0$ 0.1 $\to$ (130) 0.3 $\to$ (42) 0.5 $\to$ (22) 0.7 $\to$ (15) 0.9 $\to$ (13) 0.2 $\to$ (62) 0.4 $\to$ (29) 0.6 $\to$ (16) 0.8 $\to$ (14) 1.0 $\to$ (5) $Z=466675.399$ ${X}_{1}=1773.920$ ${X}_{2}=768039.091$ ${X}_{3}=256.143$ ${X}_{4}=17.000$ ${X}_{5}=4.000$