Reference no: EM133102240
Assessment Description
Two computer scientists-turned-farmers are planning what and how to plant during the upcoming season. There are four possible courses of action they can take, and they seek advice. In each case the outcome is either NP-complete or it can be calculated in polynomial time. You are tasked to assess the existence of a polynomial time algorithms and explain how it is assessed. If you find one, show it. If you did not find one, explain why one does not exist. You are expected to prepare professionally written answers; use rigorous mathematical notation; and include a cover page, detailed explanations, justifications for all your claims, and references.
a) There is a total of n tons of seeds to plant, with two types of crops: wheat and corn, of which they have two different quantities each, denoted by w and The farmers hope to plant an equal amount of each crop.
b) There is a total of n tons of seeds to plant, with k number of types of crops, labeled for simplicity as c1, c2, c3, ..., ck. The quantities of each crop are given by 2i, where i > 0 is an integer. The two farmers want to each plant an equal mix of crops.
c) The two farmers jointly own n boxes of seeds, of multiple crops stored in boxes of multiple weights. They want to plant the same amount of seeds each, but with the condition that they don''t split any box.
The two farmers jointly own n boxes of seeds, of multiple crops stored in boxes of multiple weights. They want to plant approximately the same amount of seeds each, and they are willing to some boxes if necessary, provided that the split is no bigger than 45%-55%.