1. Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.

2. If 1200 cm^3 of material is available to make a box with a square base and open top, find the largest possible volume of the box.

3. Find the point on the line y=4x+7 that is closest to the origin.

4. Find the point on the line 6x+y=9 that is closest to the point ( -3, 1).

5. Find the points on the ellipse 4x^2 +y^2=4 that are farthest away from the point (1,0).

6. A poster is to have an area 180 in^2 with 1-inch margins at the bottom and sides and a 2-inch margin at the top. What dimensions will give the largest printed area?