More optimization problems.

1. conehead by flickr user
greenapplegrenade
Dory Reflection- 7:33AM
by flickr user Chris Seufert
A Hat Trick of
Optimization
Wire and Wheat by flickr
user Chris & Lara Pawluk

2. Find the maximum volume of a right circular cylinder that
can be inscribed in a cone of altitude 12 centimeters, and
base radius 4 centimeters, if the centres of the cylinder
and cone coincide.

3. A person in a rowboat 2 kilometers from the nearest
point on a straight shoreline wishes to reach a
house 6 kilometers farther down the shore. If the
person can row at a rate of 3 km/hr and walk at a
rate of 5 km/hr, find the least amount of time
required to reach the house.

5. A wire 60 cm long is to be cut into two pieces. One of the pieces will be
bent into the shape of a circle and the other into the shape of an
equilateral triangle. Where shoud the wire be cut so that the sum of the
areas of the circle and triangle is minimized? maximized?