Problem. A man made lake initially contains 200 gal of water with 50 lb of a chemical dissolved into it. A solution containing 3 lb/gal of the chemical runs into the lake at a rate of 4 gal/min and the well mixed solution runs out of the lake at a rate of 4 gal/min. What is the maximum amount of chemical ever in the lake? A. Set up a differential equation modeling the amount of chemical in the lake at any time. (Choose your own notation, and clearly indicate meaning) B. Solve the differential equation. C. Based on the solution, answer the following: What is the maximum amount of chemical ever in the lake?