True or False  If P equals NP, then NP equals NP-complete.

Consider a cube defined on the following dimension hierarchies: {customer < customer_street < customer_city < customer_state} {supplier < supplier_city < supplier_state} {day < month < quarter < year} The number of cuboids that can be generated for this cube including the cuboids generated by climbing up the hierarchies along each dimension is: a. 512. b. 2048. c. 48. d. 100.

L = {f in SAT | the number of satisfying assignments of f > 1/2 |f| } Show that L is NP-complete

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. 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.