Mathematical Contest in Modeling 2013
Background
In this problem, we are asked to improve the efficiency of baking process, namely, the maximum sum area of cakes (in a certain thickness) once can be placed in an oven and the extent to which the cakes are evenly baked, through the adjustment of the shape of pans. Therefore, it involves both thermodynamics theory and two-dimensional packing problem.
Structure
Our paper is organised as follows. First, an ideal thermal model is developed to simulate the heat distribution of pans in different shapes. Next, under the requirement of maximizing the number of pans, a group of overlapped circles is used to approximately calculate the number of pans that can be placed into an oven. Finally, according to the heat distribution computed by the first model, the pan with most even distribution is selected.