CUET Mathematics 2025 22 May Shift 1 PYQs

The corner points of the bounded feasible region determined by a set of constraints (linear inequalities) are A(0, 5), B(3, 5), C(5, 0) and D(4, 1) and the objective function is z = μ + 2αρ where μ, ρ > 0. The condition on μ and α such that the maximum z occurs at B and D, is:

1. μ - 8α = 0
2. μ - 5ρ = 0
3. μ - 5α = 0
4. μ - 4ρ = 0

A manufacturing unit makes two models, 'classic' and 'supreme' of the scooter. Each piece of the classic model requires 9 labour hours for assembling and 1 labour hour for finishing. Each piece of supreme model requires 12 labour hours for assembling and 3 labour hour for finishing. For assembling and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of ₹ 10000 on each piece of the classic model and ₹ 15000 on each piece of the supreme model. Which of the following options describes the given Linear Programming Problem (LPP) to maximize the profit Z (Max Z) (where x and y are the number of pieces of the classic model and the supreme model respectively)?

The maximum value of $z$ for the linear programing problem maximize $z = x + y$ subject to the constraints $x + 4y \leq 8, 2x + y \leq 12, 3x + y \leq 9, x \geq 0, y \geq 0$ is: