A hospital is trying to decide how many new rooms to add to a new wing they are building. Each new room will contain one bed. There are currently 100 rooms.Each new room will cost $80,000 for construction and equipment. They are considering adding anywhere from 100 to 300 additional rooms, in increments of 100 rooms, giving 3 possible investment possibilities so that the hospital can remain at 100 rooms, or move to a 200, 300, or 400 room hospital. In addition to the per room construction costs, there is an additional investment cost of $3,000,000 if any additional rooms are added, no matter the number of rooms.

The decision to build is based on comparing 1/10th of this investment to some annual Contribution to investment. For instance, if 200 rooms are added, then you can think about the $19,000,000 investment as a $1.9 million annual "Cost". Suppose this was compared to an expected annual Contribution of $2.1 million, then there would be an annual surplus of $200,000. The hospital wants to make their decision based on the highest expected annual surplus, with a decision not to build anything having a $0 Contribution.

If the hospital decides to build 100 rooms, it has determined that there are two possibly future outcomes, a "Low" case with probability 0.25, and a "Medium" case with probability 0.75. (there would be no "High" case for this alternative). If the hospital decides to build either 200 or 300 rooms, it has determined that there are three possibly future outcomes, a "Low" case with probability 0.20, a "Medium" case with probability 0.65, and a "High" case for the remaining probability.

If they build 100 rooms, the Contribution used for analysis is $1.4 million for the "Medium" case and $1.3 million for the "Low" case. If they build 200 rooms, the Contribution used for analysis is $2.5 million for the "High" case, $2.3 million for the "Medium" case, and $1.0 million for the "Low" case. Finally, If they build 300 rooms, the Contribution used for analysis is $3.0 million for the "High" case, $2.8 million for the "Medium" case, and $700,000 for the "Low" case.

What decision should they make about adding rooms (how many)?