(Solved): Solve the linear programming problem using the simplex method. \[ \begin{array}{ll} \text { Maximiz ...

Solve the linear programming problem using the simplex method. \[ \begin{array}{ll} \text { Maximize } & P=3 x_{1}+2 x_{2}-x_{3} \\ \text { subject to } & x_{1}+x_{2}-x_{3} \leq 7 \\ & 2 x_{1}+4 x_{2}+3 x_{3} \leq 21 \\ & x_{1}, x_{2}, x_{3} \geq 0 \end{array} \] Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum value of \( P \) is when \( x_{1}=\quad x_{2}= \), and \( x_{3}= \) (Simplify your answers. Type integers or decimals rounded to the nearest tenth as needed.) B. There is no optimal solution.