A construction company has signed a contract to build an office tower. The contract stipulates that the project will be completed in 1500 days from today and also includes a penalty on the construction company of $30,000 per day if the project is late. In addition, the construction company estimates that its internal cost is $60,000 for each day the project is late. However, completing the project early is costly to the firm as well: each day the project is early costs the firm $45,000. (This includes opportunity cost of capital and idle capacity.) The firm estimates the project’s completion time is Normally distributed with a mean of 1400 days and a standard deviation of 60 days.
Given this data, how many days should the firm wait to begin construction? Choose the closest answer.
a. 0 days, they should start immediately
b. 50 days
c. 75 days
d. 100 days
e. 125 days