List of top Mathematics Questions on Linear Programming asked in CUET (PG)

Which of the following set is convex.
A. The set $\{(x_1, x_2) \mid \frac{x_1^2}{4} + \frac{x_2^2}{9} \le 1, x_1 \ge 0, x_2 \ge 0\}$ B. The set $\{(x_1, x_2) \mid x_1 x_2 \ge 1, x_1 \ge 0, x_2 \ge 0\}$ C. The set $\{(x_1, x_2) \mid x_1 \ge 1 \text{ or } x_2 \ge 1\}$ D. The set $\{(x_1, x_2) \mid x_1 + x_2 \le 1, x_1 \ge 0, x_2 \ge 0\}$ Choose the correct answer from the options given below:

Consider the linear programming problem
\[ Z_{\max} = 2x_1 + 5x_2 \quad \text{subject to the restrictions:} \] \[ x_1 \leq 4 \] \[ x_2 \leq 3 \] \[ 2x_1 + 3x_2 \leq 14 \] and $x_1 \geq 0, x_2 \geq 0$. Then the optimal solution is.

Maximize \( Z = 2x+3y \), subject to the constraints:
\( x+y \le 2 \)
\( 2x+y \le 3 \)
\( x,y \ge 0 \)

For the given linear programming problem,
Minimum Z = 6x + 10y
subject to the constraints
\( x \ge 6 \); \( y \ge 2 \); \( 2x+y \ge 10 \); \( x,y \ge 0 \),
the redundant constraints are:

For any Linear Programming Problem (LPP), choose the correct statement:
A. There exists only finite number of basic feasible solutions to LPP
B. Any convex combination of k - different optimum solution to a LPP is again an optimum solution to the problem
C. If a LPP has feasible solution, then it also has a basic feasible solution
D. A basic solution to AX = b is degenerate if one or more of the basic variables vanish