Optimization Assignment Water Bottle Read the instructions carefully. There are TWO parts to this assignment. PART ONE: MSeaV has hired you to design a new prototype for an environmentally friendly plastic water bottle. The water bottle is to have a volume of 750cm3. You are to consider a cylindrical model that is topped by a cone. The design would have a snip off top so no cap would be needed. For ergonomic purposes, the radius should be at least 3 cm and at most 6 cm and the height of the conical piece should be equivalent to its radius. Determine the dimensions and resulting surface area for a cone topped cylindrical plastic water bottle that minimizes the amount of plastic used. .A' Provide a solution to this problem with evidence of a plan to solve an optimization problem that includes an algebraic solution using calculus techniques (differentiation, solving for extreme values, testing interval endpoints, etc.); PART TWO: MSeaV is concerned about the cost elements associated with the manufacturing of an environmentally friendly plastic water bottle. Design criteria for the cylindrical model topped by a cone are: a volume of 750 cm3; a radius should be at least 3 cm and at most 6 cm; a height of the conical piece is to be equivalent to its radius. Associated costs are: c cylindrical lateral surface ll).0|02fcm2 (plastic); a conical surface 0.00493'cm2 (plastic and graphic); a circular base OIJDD3lcm2 (thicker plastic). Determine the dimensions, resulting cost, and resulting surface area for a cone-topped cylindrical, plastic water bottle that minimizes the overall cost to produce a bottle. Provide a solution to this problem with evidence of a plan to solve an optimization problem that includes an algebraic solution using calculus techniques (differentiation, solving for extreme values, testing interval endpoints, etc.)