Suppose you are the owner of a theater, and several different group their show would like to run, and you have an estimate of the amount of income you will make from ticket sales. Since you cannot schedule all the groups in your theater, you want to select a subset that can be scheduled and that will maximize your total estimated income from their shows s want to schedule shows in your theater. For each group, you know when Formally, this problem can be modeled as follows. You are given a collection of n tasks, each of which is represented by its time interval, [ai, bi), [az, b2), ..., [an, bn) and its corresponding weight, wi, W2,... , Wn. Task i uses interval [ai, bi) and has weight wi. In this model, the times ai, bi and weights wi are all real numbers. Design an efficient dynamic programming algorithm that finds a subset of Sci1,..., n] of the tasks that are non-overlapping, and have maximum total weight (profit). Be sure to analyze the time and space used by your algorithm. Suppose you are the owner of a theater, and several different group their show would like to run, and you have an estimate of the amount of income you will make from ticket sales. Since you cannot schedule all the groups in your theater, you want to select a subset that can be scheduled and that will maximize your total estimated income from their shows s want to schedule shows in your theater. For each group, you know when Formally, this problem can be modeled as follows. You are given a collection of n tasks, each of which is represented by its time interval, [ai, bi), [az, b2), ..., [an, bn) and its corresponding weight, wi, W2,... , Wn. Task i uses interval [ai, bi) and has weight wi. In this model, the times ai, bi and weights wi are all real numbers. Design an efficient dynamic programming algorithm that finds a subset of Sci1,..., n] of the tasks that are non-overlapping, and have maximum total weight (profit). Be sure to analyze the time and space used by your algorithm