The problem is in figure1,figure2&figure3 can be for reference only.please give the answer yo the question a,b,c,mainly question a,b.

A construction project involves the following tasks: the tasks, their estimated duration, and their immediate predecessors are shown in the table below: Our objective is to find the schedule of tasks that minimizes the total elapsed time of the project. a) Draw the task- and event-oriented networks for this problem. b) Formulate the corresponding linear program (both task and event-oriented networks) c) Solve the event-oriented LP by Excel, Python, or R codes. Although it is by no means required in order to perform the necessary computations associated with the scheduling problem, often it is useful to represent the interrelations among the tasks of a given project by means of a network diagram. In this diagram, nodes represent the corresponding tasks of the project, and arcs represent the precedence relationships among tasks. The network diagram for our example is shown in Fig. 8.5. Figure 8.5 Task-or iented network. As we can see, there are nine nodes in the network, each representing a given task. For this reason, this network representation is called a task- (or activity-) oriented network. If we assume that our objective is to minimize the elapsed time of the project, we can formulate a linearprogramming problem. First, we define the decision variables ti for i=1,2,,6, as the earliest starting times for each of the tasks. Table 8.4. gives the earliest starting times where the same earliest starting time is assigned to tasks with the same immediate predecessors. For instance, tasks 4 and 5 have task 3 as their Typically, CPM can be applied successfully in large construction projects, like building an airport or a highway, in large maintenance projects, such as those encountered in nuclear plants or oil refineries; and in complex research-and-development efforts, such as the development, testing, and introduction of a new product. All these projects consist of a well specified collection of tasks that should be executed in a certain prescribed sequence. CPM provides a methodology to define the interrelationships among the tasks, and to determine the most effective way of scheduling their completion. Although the mathematical formulation of the scheduling problem presents a network structure, this is not obvious from the outset. Let us explore this issue by discussing a simple example. Suppose we consider the scheduling of tasks involved in building a house on a foundation that already exists. We would like to determine in what sequence the tasks should be performed in order to minimize Figure 8.4 Network for a shortest-path