4.II.20C

Optimization
Part IB, 2006

Use a suitable version of the simplex algorithm to solve the following linear programming problem:

maximize50x130x2+x3 subject to x1+x2+x3302x1x235x1+2x2x340 and x1,x2,x30\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}