Lesson 24: Optimization Ii (worksheet)

Worksheet for Lesson 24 (Section 4.6) Optimization II Math 1a November 21, 2007 1. A two-liter soda bottle is roughly shaped like a cylinder a spherical cap, and is made from a plastic called polyethylene terephthalate (PET). Its volume is fixed at two liters. What dimensions of the bottle will minimize the cost of production?

Figure 1: A two-liter PET bottle

Figure 2: Liberty Island including the Statue 2. The Statue of Liberty stands on top of a pedestal which is on top of on old fort. The top of the pedestal is 47 meters above ground level. The statue itself measures 46 meters from the top of the pedestal to the tip of the torch. See Figure 2. What distance should one stand away from the statue in order to maximize the view of the statue? That is, what distance will maximize the portion of the viewer’s vision taken up by the statue?