A self-storage company is designing a new facility. The company oers two types of storage units (all rentals are for a full year):

- Medium Size: A 10x10 unit for a rental fee of $1,200 a year.

- Large Size : A 10x20 unit for a rental fee of $1,800 a year.

The new facility has a total area of 40,000 square feet and the company needs to decide how many Medium size and Large size units to build. For example, the company can build a maximum of 400 = 40,000/100 Medium size units if all the available space is allocated to this type of units. Alternatively, if all the space is allocated to Large units the company can build a maximum of 200 = 40,000/200 Large units. In general, the company can build M Medium size units and L Large size units as long as 100 M + 200 L = 40, 000.

The company believes that there is ample demand for Large size units and every Large size unit available will be rented. On the other hand, the company believe that the annual demand for Medium size units is Normally distributed with mean 250 units and standard deviation 100 units.

(a) What is the optimal number of Medium size (M) and Large size (L) units that the company should build to maximize expected rental revenues given the available space?

(b) What is the expected number of Medium size units rented in a year and the company's total expected revenues?

(c) What is the expected marginal value of an additional 200 square feet of available capacity:

(i) Less than $1,800 per year

(ii) Equal to $1,800 per year

(iii) Between $1,800 and $2,400 per year

(iv) Equal to $2,400 per year

(v) Not enough information.