Let X1 and X2 are optimal solutions of a LPP, then
Given, X1 and X2 are optimal solutions of a Linear programming problem(LPP).
This means that, {X1 ,X2} C (a convex Set) as the optimal solution of a LPP is convex.
Now by using the definition of a Convex set,
A set of points C is called convex if, for all λ in the interval 0 ≤ λ ≤ 1, λy + (1 − λ)z is contained in C whenever y and z are contained in C.
By using this property of Convex set,
If {X1 ,X2} C (a convex set of optimal solutions), then
X = λX1 + (1 − λ) X2 where 0 ≤ λ ≤ 1, is also contained in C (the optimal solution set).
This proves that, also X C.
Hence the answer is option B.