A company plans to construct a new building and parking lot on a rectangular plot of land 100 meters wide and 120 meters long. The building is to be 20 meters high and to have a rectangular footprint with perimeter 320 meters, as shown in the accompanying figure.

a. Express the volume V(x) of the building as a function of the length of its longer side x.

b. Graph the volume function in part (a), and determine the dimensions of the building of greatest volume that satisfies the stated requirements.

c. Suppose the company decides to construct the building of maximum volume. If it costs $75 per cubic meter to construct the building and $50 per square meter for the parking lot, what is the total cost of construction?

Transcribed Image Text:

100 m Building 120 m Parking lot