Show all work. 1. (4 pts) Minimize P = x2 + y', subject to x - y = 10. Justify your answer. 2. (6 pts) A lifeguard needs to rope off a rectangular swimming area in front of Long Lake Beach, using 1900 yd of rope and floats. What dimensions of the rectangle will maximize the area? What is the maximum area? (Note that the shoreline is one side of the rectangle.) Let x be the length of a side of the rectangle perpendicular to the shoreline. Justify your