Grace's bakery specializes in giant cupcakes. Each cardboard cupcake container is filled with batter and baked in the oven. The baked cupcake forms a perfect hemispherical on top of the container. The surface area of this is frosted. A clear plastic lid, identical in size and shape to the cupcake container, is then placed on top. These containers are designed such that R1=3/4R2 and h=2R1. Given that 100 cm^3 of batter costs 9cents, 100 cm^2 of frosting costs 27 cents, 100 cm^2 of cardboard costs 1.5 cents and 100 cm^2 of plastic costs 3 cents, complete the tasks below:
A.) Create functions of R1, which return the cost, in dollars, of ingredients, I, and packaging, P. Approximate all coefficients to 4 decimal places.
B.) Find the volume of a baked cupcake if Grace wants 85% of the cost to go toward ingredients. Round to 2 decimal places.
C.) Find the efficiency ratio for the packaging to the baked cupcake, to 2 decimal places.
