Consider the following project.

a$)$ Develop the project cash flow and S$-$curve diagrams for the early and late start durations

before any of the activities are crashed. For this part of the problem. You can use Excel to

develop these curves, if you like. $(33$ points$)$

b$)$ Crash the project to the least possible duration. Make sure to record the total direct cost

and duration for each iteration. $(34$ points$)$

c$)$ Assume the project overhead is $10\%$ of the total direct cost. The owner wants the project

to be completed in $24$ weeks or less and will charge a penalty of $$10,000$ for each week

of delay beyond $24$ weeks. Determine the optimum project duration and total price. $(33$

points$)$