(Solved): 21. Solve the following linear programming problem using the simplex method: Maximize \( \mathrm{P} ...

21. Solve the following linear programming problem using the simplex method: Maximize \( \mathrm{P}=15 \mathrm{x}_{1}+20 \mathrm{x}_{2} \) subject to \( 2 x_{1}+x_{2} \leq 9 \) \[ \begin{array}{r} \mathrm{x}_{1}+\mathrm{x}_{2} \leq 6 \\ \mathrm{x}_{1}+2 \mathrm{x}_{2} \leq 10 \\ \mathrm{x}_{1}, \mathrm{x}_{2} \geq 0 \end{array} \]