List of top Mathematics Questions on Linear Programming Problem asked in MHT CET

The feasible region of the linear programming problem is determined by the system of inequalities: \[ x + y \leq 6, \quad x \geq 0, \quad y \geq 0. \] What is the maximum value of \( x + y \) in the feasible region?
Maximize \( z = x + y \) subject to: \[ x + y \leq 10, \quad 3y - 2x \leq 15, \quad x \leq 6, \quad x, y \geq 0. \] Find the maximum value.