Question 1 • 2023
4 Marks
Solve graphically: Maximize and Minimize Z = 5x + 10y subject to x + 2y \le 120 , x + y \ge 60 , x - 2y \ge 0 , and x, y \ge 0 .
Answer: \text{Max } Z = 600 \text{ on segment } BC, \quad \text{Min } Z = 300 \text{ at } (60, 0)
Question 2 • 2024
4 Marks
A dietician wishes to mix two types of foods F_1 and F_2 in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food F_1 contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food F_2 contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs ₹50 per kg to purchase F_1 and ₹70 per kg to purchase F_2 . Formulate this problem as a linear programming problem and find the minimum cost graphically.
Answer: Z_{\min} = ₹380 \text{ at } (2, 4)