1. What are the advantages of analyzing and experimenting with a model as opposed to a real object or situation?
2. Suppose a manager must choose between the following two mathematical models of a given situation: (a) a relatively simple model that is a reasonable approximation of the real situation and (b) a thorough and complex model that is the most accurate mathematical representation of the real situation possible. Why might the model described in part (a) be preferred by the manager?
3.The O’Neill Shoe Manufacturing Company will produce a special-style shoe if the order size is large enough to provide a reasonable profit. For each special-style order, the com- pany incurs a fixed cost of $2000 for the production setup. The variable cost is $60 per pair, and each pair sells for $80. a. Let x indicate the number of pairs of shoes produced. Develop a mathematical model
for the total cost of producing x pairs of shoes.
b. Let P indicate the total profit. Develop a mathematical model for the total profit real- ized from an order for x pairs of shoes.
c. What is the breakeven point?
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