Prove that optimal Solution exist without solving.

Question

![1]: https://i.stack.imgur.com/Osa3G.jpg

Without solving the problem, show that it has an optimal solution.

Answer 1

1. Using all the Basic Feasible solutions(BFS), found in first part.
2. From theorem [1] , every BFS <=> extreme point of feasible set
3. From theorem [1], If an LPP has an optimal solution then it has an optimal solution at an extreme point of the feasible set.