9. A new engineering building at a state university is to contain 10,000,000 square feet. The total cost of the building (TC) is given by the following expression:

TC 5 1200 1 80X 1 2X22A where X 5 number of fl oors and A 5 fl oor area in ft2/fl oor.

a. Create a table that shows the total building cost, average cost per fl oor, and marginal cost per fl oor (using the difference equation approach) for confi gurations ranging from 1 fl oor to 12 fl oors, inclusive. (Hint: You may want to create the table using your favorite spreadsheet program.)

b. Based on your table, what is the optimal number of fl oors for the building?

Justify your answer based on the ‘‘total cost’’ column.

c. Justify your answer in Part b based on the ‘‘marginal cost per fl oor’’ column.

d. Demonstrate, using differential calculus, that your answer in Parts b and c is correct. (Note: For this part, assume that X is a continuous variable.)