Hello. I need help with these questions related to linear programming. Any help will be apreciated

1. 8 marks There are five independent questions below. What can you say about the dual if you already know: (answer for each of the following considered individually) a) a feasible solution to the primal exists? b) an optimal solution to the primal exists? c) an optimal solution a* = (ri, ...,x* ) to the primal exists with rt > 0? d) an optimal solution a* = (r), ...,x*, ) to the primal exists with rt = 0? e) there is no feasible solution to the primal? You have to justify / explain your answer. Especially, you have to give the precise names of the theorems you use