MSeaV has hired you to evaluate the cost-efficiency of a newly /'\\\\ designed, environmentally friendly, plastic water bottle. The water bottle prototype is cylindrical with a hemispherical top, and has a puncture hole, so no cap would be needed. You are given the following information. Design criteria for ergonomic purposes : I bottle must be able to hold 750cm3 of water. I the radius should be at least 3 cm and at most 6 cm. Associated Costs: I cylindrical lateral surface (plastic) 0.0015(1:,icm2 I hemispherical surface (plastic and graphic) 0.005(1'Jcm2 I circular base (thicker plastic) 0.003/cm2 Determine the dimensions and surface area for this model that would minimize the overall cost to manufacture this bottle. Round all nal answers to two decimal places. However, you may need to increase accuracy with an extra decimal place when comparing costs Provide an algebraic solution using calculus techniques (differentiation, solving for extreme values, testing interval endpoints, etc.)