1. You have signed a contract that gives you a payment for 100,000 for a project. Suppose this project can be broken down into two serial activities - A and B. The time taken by activity A is uniformly distributed between 10 days and 60 days.

Activity B takes exactly 50 days to complete if worked on by 2 people.

But you may choose to have more people work on activity B and reduce the time it takes to complete. Specifically, you calculate that it would take 40 days to complete if worked on by 3 people.

The extra cost of this additional person for working on activity B is $1500

The contract you signed with your client is structured so that a quadratic penalty gets deducted based on how many days you take to complete the project.

Specifically, if your project gets completed in 70 days, your net payment would be $100,000 minus (70)² = 100,000 - 4900 = $95,100

Similarly, if your project gets completed in 80 days, your net payment would be $100,000 minus (80)² = 100,000 - 6400 = $93,600

1. What is the expected value you receive if you choose to use only 2 people on activity B?
2. What is the expected value you receive if you choose to use 3 people on activity B?

You decide to run the project as follows: you will defer making the choice of whether or not have 3 people work on activity B.

Specifically, you decide that if activity A takes less than 20 days to complete, then you will use only 2 people to work on activity B. if it takes more than 20 days to complete, then you will use 3 people to work on activity B.

1. What is the expected value of following the above strategy?

Change the number of days you defer the choice from 20 days (as give above) to other values. For instance, try deferring the choice for 25 days, 30 days, 35 days, ....

1. From the above, how many days should we defer the choice?
2. Finally, will the optimal length of time you delay making the choice increase or decrease if the cost of the additional person is $1800 (instead of $1500 that you used for your prior questions).