NP-completeness of an optimization problem on plants selection using reduction method

Non-determinism is a challenging feature of a group of problems in computer science. It includes optimisation problems, graph theory based problems, decision problems etc. Finding out the solvable of problems in computer science is one of the predominant motive to start with research on such problems. In theoretical computer science there are different methods to find out the solvability of the problems. Checking whether a problem is similar to standard problems through a well defined systematic way of reduction process, we are able to formulate various proofs for the problem under consideration. This work addresses a problem in an optimization domain which deals with the selection of plants from a given set of plants. Even though the problem statement appears to be simple, the reduction process modeling is quite challenging in the sense to find out various dimensions of objective functions, constraints and decisions to find out minima and maxima of functions etc. It gives an insight into the solvability of a real world problem by a theoretical approach. The whole work is done to determine an objective function and reduce the problem to a standard NP-Complete problem to decide the solvability of the current problem.