1) A fence is to be constructed along the side of a 100ft barn so as a rectangular area (as shown in the diagram). What is the maximum area that can be constructed if the total length of fencing to be used is 240ft? What are the dimensions of the fenced-in area?

2) There are currently 20 muppet trees in an orchard capable of growing up to 30 trees. Each tree produces 60 muppets. For each additional tree we plant, the output per tree drops by 2 muppets. What is the optimal number of trees in the orchard (assuming we want to maximize the number of muppets produced)?

3) Find the point on y = 2x closest to the point (6,0).