Working on Linear Programming Problems - Operations Management Help

$\frac{1}{100}{{x}^{2}}+5x-3\ge 0$
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$f\left( x \right)=\frac{1}{100}{{x}^{2}}+5x-3$
$\frac{1}{100}{{x}^{2}}+5x-3\ge 0$ $x\ge 0.599282$ $\begin{array}{cc} & 420\left( {{x}_{i}}-{{x}_{i+1}} \right)+180\left( {{x}_{i}}-{{x}_{i+1}}-10 \right)-{{t}_{i}}\le 0 \\ & 420\left( {{x}_{i}}-{{x}_{i+1}} \right)+180\left( {{x}_{i}}-{{x}_{i+1}}-10 \right)+1400\left( {{x}_{i}}-{{x}_{i+i}}-30 \right)-{{t}_{i}}\le 0 \\ \end{array}$ $\begin{array}{cc} & 600\left( {{x}_{i}}-{{x}_{i+1}} \right)-{{t}_{i}}\le 1,800 \\ & 2,000\left( {{x}_{i}}-{{x}_{i+1}} \right)-{{t}_{i}}\le 43,800 \\ \end{array}$ end
x1 < 1
x2< 1
x3<1
x4< 1
$\begin{array}{cc} & Maximize\,\,\,\,3{{x}_{1}}+6{{x}_{2}}+25{{x}_{3}}+60{{x}_{4}} \\ & s.t.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,24{{x}_{1}}+76{{x}_{2}}+43{{x}_{3}}+754{{x}_{4}}\le 806 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,755{{x}_{1}}+27{{x}_{2}}+33{{x}_{3}}+67{{x}_{4}}\le 806 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{1}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{2}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{3}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{4}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{i}}\ge 0 \\ \end{array}$ $\begin{array}{cc} & Maximize\,\,\,\,3{{x}_{1}}+6{{x}_{2}}+25{{x}_{3}}+60{{x}_{4}} \\ & s.t.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,24{{x}_{1}}+76{{x}_{2}}+43{{x}_{3}}+754{{x}_{4}}\le 806 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,755{{x}_{1}}+27{{x}_{2}}+33{{x}_{3}}+67{{x}_{4}}\le 806 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{1}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{2}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{3}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{4}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{i}}\in \{0,1\} \\ \end{array}$

$\begin{array}{cc} & Minimize\,\,\,-\,3{{x}_{1}}-6{{x}_{2}}-25{{x}_{3}}-60{{x}_{4}} \\ & s.t.\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,24{{x}_{1}}+76{{x}_{2}}+43{{x}_{3}}+754{{x}_{4}}\le 806 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,755{{x}_{1}}+27{{x}_{2}}+33{{x}_{3}}+67{{x}_{4}}\le 806 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{1}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{2}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{3}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{4}}\le 1 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}_{i}}\in \{0,1\} \\ \end{array}$