Which of the following statements is correct?
Given,
The statements:
• Every LPP admits an optimal solution
This need not be true as all LPPs need not have optimal solutions and such LPPs are called unbound.
• A LPP admits unique optimal solution
Every LLP need not have unique optimal solutions as if there are two optimal solutions to an LLP there will be infinite number or optimal solutions to the LLP problem.
• If a LPP admits two optimal solutions it has an infinite number of optimal solutions
As mentioned in the above point, if there are two optimal solutions to an LLP there will be infinite number or optimal solutions to the LLP problem.
• The set of all feasible solutions of a LPP is not a convex set.
As per a theorem of Convex Sets,
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 makes all the feasible solutions of a LPP also a convex set.
Hence, from the explanations, the answer is Option C.