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The number of solutions for the following system of inequalities is

• $X_1≥ 0$
• $X_2 ≥ 0$
• $X_1+ X_2 ≤ 10$
• $2X_1+ 2X_2 ≥ 22$
1. $0$
2. infinite
3. $1$
4. $2$

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$X_1 ≥ 0\quad \to (1)$
$X_2 ≥ 0\quad \to (2)$
$X_1 + X_2 ≤ 10\quad \to (3)$
$2X_1 + 2X_2 ≥ 22 \quad \to(4)$

Now the equation $(4)$ can be written as
$X_1 + X_2 ≥ 11 \quad \to (5)$

Now, equations $(3)$ and $(5)$ cannot hold true together since $X_1 ≥ 0$ and $X_2 ≥ 0.$
Hence, system of inequalities can never be satisfied.

Answer A. $0$

by Loyal (9.7k points)
selected by
+1
Although answer is trivial. But in complex question in such category could be solved by drawing appropriate graph.
0
may you draw pls ?
+1 vote
Equations can be written in $AX=B$ form.
Rank of augmented matrix $AB$ is $3$ and rank of $A$ is $2$ so the system of non-homogeneous equations is inconsistent.
So, no solution exists.

Option A.
by Junior (913 points)