1. The problem statement, all variables and given/known data The first problem is a related rates question: A swimming pool if 5m wide and 25m long, 1m deep at the shallow end and 4.5 deep at the deepest point. A cross section is shown in the figure below. The pool is being filled at a rate 0.5m^3/hr. Use calculus techniques to find out how fast is the water level rising when the depth at the deepest point is 2.5m. I understand we want to find dh/dt when h at the deepest point is 2.5m. I know we are provided with dv/dt but I am absolutely clueless as to how to find out dh/dv! The second question I found even more challenging... A closed box of a square base and rectangular sides is to have a volume of 1000cm^3. If the material used for the dies of the box is 20% more expensive per square meter than the material on the bottom, and the material to produce the top costs 50% more per square meter than that of the bottom, find the most economical proportions of the box. I'm totally clueless in this one and have absolutely no idea where to start.