Your company needs to execute the following project:

Activity	A1	A2	A3	A4	A5	A6	A7	A8
Duration (in days)	20	13	15	9	20	30	20	25
Predecessors	--	A1	A1	A1	A2,A3	A4,A5	A4,A5	A6,A7

For b, c and d assume that each task is normally distributed with the given expected duration. The standard deviation of each task is 40% of its expected duration (for example, the standard deviation of task A1 is 8).

1. Using a simulation with 1000 trials, what is the expected duration of the project? What is the expected standard deviation? (10 points)

1. Assume an income of $100,000 for delivering the project (at any point in time). Your project's cost is fixed at $50,000. If the project is delivered in more than 110 days, your company will incur a penalty of $10,000. If the project is delivered in more than 120 days, your company will incur a penalty of $35,000. There are no double penalties (that is, if the project is delivered on day 123, for example, there is only one penalty: $35,000). Use the simulation to determine the expected income. (20 points)
2. Assume your company can outsource the project to a sub-contractor. The sub-contractor commits to the following: if he delivers the project within 110 days, he receives $100,000 from your company. If he delivers the project in more than 110 days, he receives nothing.

Note that if you outsource the project you don't incur the project costs mentioned in c (since your company is not the one actually executing the project). Even if you outsource the project, your company will still receive the $100,000 income once the project is done (since you are the main contractor) and may incur the penalties (the $10,000 and the $35,000) if the project is late.

What is your expected income if you use the sub-contractor? Would you outsource the project to the sub-contractor? (20 points)