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MODEL PAPER 2025 — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSMODEL PAPER 20253 Marks
Question
Consider the following Linear Programming Problem:
Minimise Z = x + 2y
Subject to $2 x+y \geq 3, x+2 y \geq 6, x, y \geq 0$
Show graphically that the minimum of Z occurs at more than two points
✓

Answer

The feasible region determined by the constraints$2 x+y \geq 3, x+2 y \geq 6, x \geq 0, y \geq 0$ is as shown.
Image
The corner points of the unbounded feasible region are A(6, 0) and B(0, 3) The values of Z at these corner points are as follows:

 Corner point Value of the objective function z = x + 2y
 A(6, 0) 6
 B(0, 3) 6

We observe the region x + 2y < 6 have no points in common with the unbounded feasible region. Hence the minimum value of z = 6
It can be seen that the value of Z at points A and B is same. If we take any other point on the line x + 2y = 6 such as (2,2) on line x+ y = 6 then Z = 6
Thus, the minimum value of Z occurs for more than 2 points, and is equal to 6.

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