(16 points) A farmer has $1236 to enclose a rectangular field with a fence. It will cost $2 per yard to fence the widths and $3 per yard to fence the lengths. Find the dimensions of the rectangle that will maximize the area of the field.(10 points) A 5-meter piece of lumber is leaning against a wall at a construction site. If the bottom of the lumber slides away from the wall at a rate of 0.1 meters per second, how fast is the top of the lumber sliding down the wall, when the bottom of the lumber is 4 meters from the wall