A manufacturer hires your engineering firm to design a cylindrical soup can that will hold 10 oz (296ml) of soup and will include a plastic lid to reseal the can. The manufacturer seeks the dimensions in centimeters that minimize total cost of the can. The cost for the materials is as follows: Material Cost Top of can (thin plastic, removable) $0.00125/cm2 Curved side of can and bottom $0.0005/cm2 Label $0.000025/cm2 (Assume this is an exact fit to the curved side of the can with no overlap) Bottom and side solder $0.005/cm (Assume this is used on the vertical side seam and the circular bottom seam) Glue for the seam of the label and top $0.00025/cm (Assume this is used along the vertical seam of the label and around the top, to seal the plastic covering) Plastic lid $0.002/cm2 (Assume the cost of the lip of the lid is included in this) Complete the following and show all work: State the function to be optimized, in terms of pi and the radius and height of the can using the following as a guide as stated in Q2-Q9. Completely simplify