Exam Questions & Step-by-Step Markschemes (8 Problems)
Question 1 • 2024
5 Marks
Solve the following Linear Programming Problem graphically: Maximize and Minimize Z = 5x + 10y subject to the constraints: \begin{aligned} x + 2y &\le 120 \\ x + y &\ge 60 \\ x - 2y &\ge 0 \\ x, y &\ge 0 \end{aligned}
Answer: Z_{\min} = 300 \text{ at } (60, 0), \quad Z_{\max} = 600 \text{ at all points along segment } BC
Question 2 • 2024
5 Marks
Solve the following Linear Programming Problem graphically: \text{Minimize and Maximize } Z = 5x + 10y subject to the constraints: \begin{aligned} x + 2y &\le 120 \\ x + y &\ge 60 \\ x - 2y &\ge 0 \\ x, y &\ge 0 \end{aligned}
Answer: \text{Minimum } Z = 300 \text{ at } (60, 0); \quad \text{Maximum } Z = 600 \text{ at all points on line segment joining } (60, 30) \text{ and } (120, 0)
Question 3 • 2024
5 Marks
Solve the following linear programming problem graphically: \text{Maximize } Z = 4x + 3y subject to the constraints: x + y \le 50 3x + y \le 90 x \ge 0, \quad y \ge 0
Answer: Z_{\max} = 170 \quad \text{at } (20, 30)
Question 4 • 2024
5 Marks
Solve the following Linear Programming Problem graphically: \text{Maximize } Z = 4x + y Subject to constraints: \begin{aligned} x + y &\le 50 \\ 3x + y &\le 90 \\ x \ge 0, &\quad y \ge 0 \end{aligned}
Answer: Z_{\max} = 120 \quad \text{at } x = 30, \; y = 0
Question 5 • 2023
5 Marks
Maximize Z = x + 2y subject to 2x + y \le 10 , x + 2y \le 8 , and x, y \ge 0 .
Answer: \text{Maximum } Z = 8 \text{ (along line segment joining } (0, 4) \text{ and } (4, 2))
Question 6 • 2024
5 Marks
Solve the following Linear Programming Problem graphically: \text{Maximize } Z = 250x + 70y subject to the constraints: \begin{aligned} 3x + y &\le 66 \\ x + y &\le 45 \\ x &\ge 0, \quad y \ge 0 \end{aligned}
Answer: Z_{\text{max}} = 5500 \quad \text{at } (22, 0)