Suppose you are assigned to manage the house$-$building project, whose details are shown in the following table. Draw the project diagram, and find the critical path, total duration, and total float and

free float for every activity.

b$)$ Suppose you are expected to finish the project within $20$ days. You find you have to

hire more workers in order to shorten the total duration. Please find the minimum cost

to achieve the goal. The cost table is shown as follows