1. Optimization Problems Section 4.5

2. Find the dimensions of the rectangle with maximum area that can be inscribed in a semicircle of radius 10.

3. A rectangular field is to be bounded by a fence on three sides and by a straight stream on the fourth side. Find the dimensions of the field with the maximum area that can be enclosed with 1000 feet of fence.

4. A closed rectangular container with a square base is to have a volume of 2000 cubic centimeters. It costs twice as much per square centimeter for the top and bottom as it does for the sides. Find the dimensions of the container of least cost.

5. Suppose that the intensity of a point light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. Two point light sources with strengths S and 8S are separated by a distance of 90 cm. Where on the line segment between the two sources is the intensity a minimum?