$4.$ A firm$$s three clients each requested the firm to conduct a project. Four available managers can be assigned to these three projects. Each of them can handle only one client. The following is the number of hours required for each manager to complete each project based on their experience and expertise. Manager $2$ is still working on her certificate and cannot serve Client C yet. $(15$ pts$)$ a$.$ Draw the network representation of the problem. b$.$ Formulate a linear program to minimize the total number of hours required. Client Manager A B C $12503102702270350--3280330225$