(Solved): Solve the linear programming problem by the simplex method. Maximize \( 60 x+45 y \) subject to the ...

Solve the linear programming problem by the simplex method. Maximize \( 60 x+45 y \) subject to the following constraints. \[ \left\{\begin{array}{r} x+y \leq 5 \\ -2 x+3 y \geq 6 \\ x \geq 0, \quad y \geq 0 \end{array}\right. \] Put the second constraint into \( \leq \) form. \[ \left\{\begin{array}{ccc} x+ & y \leq & 5 \\ 2 x+(-3) y \leq & -6 \\ x \geq 0, & y \geq 0 \end{array}\right. \] Construct the corresponding linear system. \[ \left\{\begin{array}{ccc} x+y+u & = & 5 \\ 2 x+(-3) y+v & = & -6 \\ -60 x+(-45) y+M & =0 \end{array}\right. \] The maximum value of \( \mathrm{M} \) is , which is attained for \( \mathrm{x}= \) and \( \mathrm{y}= \)