Economic Design A: Cone-topped Cylinder Instructions 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: volume of 750 cm3: radius should be at least 3 cm and at most 6 cm; . M Sen V height of the conical piece is to be equivalent to its radius. 4 You Associated costs are: cylindrical lateral surface 0.002c/cm (plastic); conical surface 0.004c/cm= (plastic and graphic); circular base 0.003c/cm= (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.);