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: 0 volume of 750 cm3; o radius should be at least 3 cm and at most 6 cm; 0 height of the conical piece is to be equivalent to its radius. Associated costs are: 0 cylindrical lateral surface 0.002931ch (plastic); 0 conical surface 0.004lcm2 (plastic and graphic); 0 circular base 0.003gill'cm2 (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)