CUET Mathematics 2025 21 May Shift 1 PYQs

A linear programming problem is as follows:

Minimize $z = 2x + 3y$

Subject to the constraints $x \ge 3, x \le 9, y \le 10, x - y \ge 0, x + y \le 14$. The feasible region has 5 corner points including

The corner points of the feasible region determined by a system of linear constraints are $(0, 0)$, $(0, 40)$, $(20, 40)$, $(60, 20)$, $(60, 0)$. If the objective function is $z = 4x + 3y$, then which one of the following is true?

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)?