1) A rectangular garden is bounded on one side by a river and is to be fenced in on the three other sides. Fencing material for the side parallel to the river is $30 per foot. Materials for the two other sides cost $10 per foot. What are the dimensions of the garden of largest possible area if $1200 is to be spent for fencing material?
2) A rectangular piece of cardboard measuring 20 inches by 32 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each square. What is the maximum volume of this box?