1. An airplane ticket costs $200 if there are 50 or fewer people on the plane. But for each passenger over 50, the price per ticket is reduced by $2. (For example, if there are 52 passengers, then a ticket costs $196.) If revenue is maximized, how many people would be on the plane?
2. Determine the point(s) on the curve y = x2 + 1 that are closest to (0, 2).
3. Let x and y be positive numbers whose sum is 50 (i.e., x + y = 50). What is the largest possible value of the product xy?
4. The number of bacteria N grows according to the formula N(t) = 6000t , where t 60+t2 is measured in weeks. What is the maximum size of the population, and when does this happen?
5. How fast does the water level drop when a cylindrical tank with a radius of 6 feet is drained at a rate of 3 ft3/min? (The volume V of a cylinder is V = πr2h, where r is the radius and h is the height of the cylinder.)