When baking a cake in a square pan, the heat will be concentrated at four corners, and the food will be burnt at four corners (even the edges). In a round pan, the heat will be evenly distributed throughout the outer edge, so that the food will not be burnt by the edge. However, because most ovens are rectangular, it is not very effective to use a round pan. Establish a model to show the heat distribution at the outer edge of pots with different shapes-including shapes from rectangle to circle and middle.

Try to build a model to show the heat distribution at the outer edge of different pot bottoms: square to round and other shapes in the middle.

Suppose:

1. The length-width ratio of a square oven is w/l;

2. The area of all reference basins must be a;

3. At first, the two brackets of the oven are balanced.

Create a model to screen the best flowerpot type under the following conditions:

1. Maximum number of ovens (n);

2. Pot shape (H) that maximizes uniform heat distribution;

3. Optimization conditions (1) and (2) with occupancy rates of p and (1- p) respectively are used to describe the difference between W/L and p.

In addition to providing standard answers in MCM format, you also need to highlight your design and results by providing 1-2 pages of advertisements for Brownie Food Magazine.

B: the shortage of available fresh water resources

The shortage of fresh water resources has become a bottleneck in the development of many countries in the world.

Establish a mathematical model of a country's water resources strategy in 20 13 years, determine an efficient, practical and cost-effective water resources strategy to meet the country's expected water resources demand in 2025 (the United States, China, Russian, Egyptian or Saudi Arabia, choose one), and determine the best water resources strategy. In particular, the mathematical model you build must consider the country's water resources reserves and flow laws, the development of seawater and fresh water treatment and the protection of water resources. If possible, discuss the possible economic, geographical and environmental impacts of this model by applying your model, and provide a non-technical government position report for the country's leadership. In the report, you will briefly introduce your method, the feasibility and cost accounting of this method, and why this party is the "best strategic choice".

Choice of country: USA, China, Russian, Egyptian or Saudi Arabia.