CUET Mathematics 2026 22nd May Shift 1 PYQs

An objective function $Z=a x+b y$ is maximum at points $(8,2)$ and $(4,6)$. If $a \geq 0$ and $b \geq 0$ and $a b=25$, then the maximum value of the function is equal to :

About linear programming problem (LPP), which of the following statements are correct?

(A) In a LPP, the linear inequalities or restrictions on the variables are called linear constraints.

(B) If the feasible region for an LPP is unbounded, then the maximum or minimum value of the objective function $Z = ax + by$ never exists.

(C) The feasible region for an LPP is always convex.

(D) The common region determined by all the linear constraints of an LPP is called the feasible region.

Choose the correct answer from the options given below:

A manufacturing company makes two models M$_1$ and M$_2$ of a product. Each piece of M$_1$ requires 9 labour hours for fabricating and one labour hour for finishing. Each piece of M$_2$ require 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs.800 on each piece of M$_1$ and Rs.1200 on each piece of M$_2$

The maximum profit will be at the point