What could make a good model for this situation? Using Polya’s technique for solving problems, describe and discuss the strategy, steps, and procedures you will use to solve this problem

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Mathematical Modeling
and Problem Solving

All commonly used formulas for geometric objects are really
mathematical models of the characteristics of physical objects. For example, the
characteristic of the volume inside a common closed cardboard box can be
modeled by the formula for the volume of a rectangular solid, V = L x W x H,
where L = Length, W = Width, and H = Height of the box. A basketball, because
it is a sphere, can be partially modeled by its distance from one side through
the center to the other side, or diameter, by the diameter formula for a
sphere, D = 2r.

Complete onlyONE
of the following questions.

1. (Please review Chapter 9 in the College Math
   text for geometric objects and their properties.) For a familiar example, the
   perimeter and area formulas for a rectangle are mathematical models for
   distance around the rectangle (perimeter) and area enclosed by the sides,
   respectively; P = 2L + 2W and A = L x W. For another example, the volume of a rectangular
   box would be: V = L x W x H, where L = Length, W = Width, and H = Height. The surface
   area of a rectangular box would be: SA = 2(L x W) + 2(W x H) + 2(L x H). Your
   problem is to obtain (or make) a rectangular
   box with a top on it that has the smallest possible surface area and that a
   football and a basketball, both fully inflated, will just fit into at the same
   time. What could make a good model for this situation? Using Polya’s technique
   for solving problems, describe and discuss the strategy, steps, and procedures you
   will use to solve this problem. Then, demonstrate that your solution is
   correct.