Problem of the Week-7: Minimize Travel Time
Under new building codes, some building designs minimize the travel time from an extreme corner of the top floor of a building to the lower most opposite corner on the ground floor.
Consider a multilevel rectangular building with square floors (a square base) each of the same size. Given that the average speed of walking is 5 ft per second, and if the average elevator speed is 20 ft per second (The "speed" of elevator in Hayes is nowhere near this!) and the total volume of the building is to be 1,492,992 ft^3, find the dimensions of the building that minimize the travel time to opposite corners of the building. Assume that a person walking across any floor walks in hallways that are perpendicular to each other (so no diagonal shortcuts, also no backtracking). Also assume that there is no time lost waiting on elevators (not a very realistic assumption but ...)
Explain your answer and show your steps.
Submit your answers (by e-mail or hard copy) before 4 pm on 12/8/06 to Noah Aydin.