X_{1 }≥ 0 ...[1]
X_{2}_{ }≥ 0 ...[2]
X_{1 }+ X_{2 }≤ 10 ...[3]
2X_{1 }+ 2X_{2 }≥ 22 ...[4]
Now the equation [4] can be written as
X_{1 }+ X_{2 }≥ 11 ...[5]
Now equation [3] and [5] cannot hold true together since X_{1 }≥ 0 and X_{2}_{ }≥ 0.
Hence system of inequalities can never be satisfied.
Hence Answer A)0