Term Project Your job is to design a open topped, rectangular box of minimum cost. Suppose the box is to be of volume V0 cubic cm; and the cost of material for the front and back sides is b dollars per square cm, c dollars per square cm for the left and right two sides, and d dollars per square cm for the bottom side. Note that V0 , b, c and d are just arbitrary constants. Treat them just like they were numbers! 1) Do the mathematics to find the dimensions of the box of minimum cost. Show this work in the appendix of the paper. 2) Explain the ramifications of various differences in the costs of materials, i.e. what happens to the dimensions of the box. Consider these three cases: i) b = c = d, ii) 2b = 2c = d, iii) b = c = 2d. 3) Write your results in a report (as if you were conveying this information to your boss) that would be appropriate for someone that doesn't understand calculus. 4) Include all the pertinent mathematics in an appendix that will be attached to the report. 5) The report part (excluding the appendix) should be 3-7 pages. 6) The appendix should include all the necessary work you made to come up with your solution. Note! The text material necessary to do the mathematics involved in this project is contained in section 14.7 (Do not use the methods from section 14.8). Also please include the analysis to justify that your dimensions give a minimum cost