A carpenter is building a rectangular room with a fixed perimeter of 324 ft. What dimensions would yield the maximum area? What is the maximum area?

Ben’s Bicycle Designs has determined that when x hundred bikes are built, the average cost per bike is given by C(x)=0.5x^2 – 1.6x+5.597, where C(x) is in hundreds of dollars. How many bikes should the shop build to minimize the average cost per bike?