1) A fence 2 feet tall runs parallel to a tall building at a distance of 7 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?
2) The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 448 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 4 dollar increase in rent. Similarly, one additional unit will be occupied for each 4 dollar decrease in rent. What rent should the manager charge to maximize revenue?
3)If 2400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
4) Find the point on the line 2 x + 7 y + 2 =0 which is closest to the point ( 5, 5 )