Suppose you want to fence in a rectangular shaped region along the straight edge of a river. The side along the river does not need to be fenced. In addition, the region will be subdivided into two parts. The fencing material that will be used for the three sides that are perpendicular to the river costs $5 per linear foot, and the fencing for the other side costs $10 per linear foot. Suppose you have $450 to spend on fencing. Find the dimensions of the total region that will provide the maximum area. What is the maximum area?