I have just invented a new coffee drink called Chock Full of Protein(CPP). CFP is produced in an instant powder form that has a density of 450 kg/m". I need 16 ounce pnclonge designed for CPP so that I may start marketing CFP to the world. I have the choice of several currently used designs that other manufacturers se for coffee or protein powder. Most are a cylindrical shape or a rectangular print shapelike bricks of coffee) I want the cost to produce CFP to be minimal. Your job is to find which type of package to use. In order to minimize cost the surface are must be as small as possible and still be able to hold the required 16 ounces 1. Modeling Stage (a) (10 points) Work out at the three possibilities for a CFP package: a cylinder, a fustrum, and rectangular prism. If a fustrum is chosen, there are two extra requirements due to astetics. First, the base radius should be 3 times the top radius. Second, girth of the fustrum can't exceed 314 cm. No other requirements are given for the other two packages. (b) (10 points) Make a sketch of each package. Label with all possible variables. (c) (20 points) Find a function for each package that will be optimized in the context of the problem Analysis Stage (10 points) Graph the functions found in parte. Find an appropriate domain in context of the problem (P (20 points) Use the optimization techniques from class to find the critical values and Identify the minimum or maximum of the function. I have just invented a new coffee drink called Chock Full of Protein(CPP). CFP is produced in an instant powder form that has a density of 450 kg/m". I need 16 ounce pnclonge designed for CPP so that I may start marketing CFP to the world. I have the choice of several currently used designs that other manufacturers se for coffee or protein powder. Most are a cylindrical shape or a rectangular print shapelike bricks of coffee) I want the cost to produce CFP to be minimal. Your job is to find which type of package to use. In order to minimize cost the surface are must be as small as possible and still be able to hold the required 16 ounces 1. Modeling Stage (a) (10 points) Work out at the three possibilities for a CFP package: a cylinder, a fustrum, and rectangular prism. If a fustrum is chosen, there are two extra requirements due to astetics. First, the base radius should be 3 times the top radius. Second, girth of the fustrum can't exceed 314 cm. No other requirements are given for the other two packages. (b) (10 points) Make a sketch of each package. Label with all possible variables. (c) (20 points) Find a function for each package that will be optimized in the context of the problem Analysis Stage (10 points) Graph the functions found in parte. Find an appropriate domain in context of the problem (P (20 points) Use the optimization techniques from class to find the critical values and Identify the minimum or maximum of the function