List of top Mathematics Questions on Linear Programming asked in PSEB XII

Solve the following linear programming problem graphically: Maximise and minimise \( Z = 4x + 2y - 7 \) subject to the constraints: \[ x + 3y \leq 60, \quad x + y \geq 10, \quad x - y \leq 0, \quad x \geq 0, \quad y \geq 0 \]

Objective function of a L.P.P is a function to be optimized.

Maximum value of \( Z = 3x + y \) for the constraints \( x + y \leq 4, x \geq 0, y \geq 0 \) is:

Objective function of a linear programming problem is:

Solve the following linear programming problem graphically: Maximize and minimize \( Z = 4x + 2y - 7 \) subject to the constraints \( x + 3y \le 60, x + y \ge 10, x - y \le 0, x \ge 0, y \ge 0 \).
Correct Answer: Max Value \( Z = 73 \) at \( (15, 15) \); Min Value \( Z = 13 \) at \( (5, 5) \). (Based on standard corner point analysis)

Objective function of a linear programming problem is: