4.II.20COptimizationPart IB, 2006Use a suitable version of the simplex algorithm to solve the following linear programming problem:maximize50x1−30x2+x3 subject to x1+x2+x3≤302x1−x2≤35x1+2x2−x3≥40 and x1,x2,x3≥0\begin{array}{lrrrrr}\operatorname{maximize} & 50 x_{1} & - & 30 x_{2}+x_{3} & \\ \text { subject to } & x_{1}+ & x_{2}+x_{3} & \leq 30 \\ & 2 x_{1} & - & x_{2} & & \leq 35 \\ & x_{1} & + & 2 x_{2} & -x_{3} & \geq 40 \\ \text { and } & & & x_{1}, x_{2}, x_{3} & \geq 0\end{array}maximize subject to and 50x1x1+2x1x1−x2+x3−+30x2+x3≤30x22x2x1,x2,x3−x3≥0≤35≥40