I have four word problems that are due tomorrow, and my main problem is that I can't figure out how to get the formulas. We have to somehow end up with a quadratic that we can get a first and second derivative from in order to find a max or min. If someone could at least help out with the formulas, I should be able to solve the rest of the problem. I especially don't understand 2 and 4, so if anyone could try to explain them, it would be much appreciated.
1. A chartering company will provide a plane for a fare of $300 per person for 100 or fewer passengers (but more than 60 passengers.) For each passenger over 100, the fare is decreased $2 per person for everyone. What number of passengers would provide the greatest revenue?
2. At noon, ship A, steaming east at 10 knots, is 130 nautical miles due north of ship B, which is steaming north at 15 knots. When will the ships be closest together?
3. A box of volume 32 cubic feet having a square base and no top is to be constructed from materials costing $1.00 per square foot. Find the dimensions of such a box for which the cost of material is least.
4. Find the point on the parabola y=x^2 that is closest to the point P(3,0).