Assume you are given a set of activities that wish to use a resource, and that each activity takes unit time. At any instance = 1,2 , only one activity can use the resource. Assume that activity , = 1 , earns a profit of if and only if it is executed no later than time (no profit is earned if activity is executed after ). The goal is to execute a set of activities that maximizes profit. Discuss how this problem possesses the elements necessary for a greedy solution, and prove that the greedy solution is optimal. Provide a detailed description of a solution that solves this problem as efficiently as possible.