Question: In a retailing operation, total costs can be expressed as a function of total sales. A small store found recently that when their total sales increased from $1,000 to $4,000, their costs increased from $750 to $1,500.

1. Which is the dependent variable and which is the independent variable? Explain.
2. Assuming that a linear functional relationship exists, determine the equation that relates total costs to total sales.
3. As long as the total revenue is between $0 and $5,000, this relationship is expected to hold. Graph the function over the appropriate range.
4. Explain why the nature of the relationship may change if sales exceed $5,000.
5. Find and interpret C(2,000).
6. Calculate the profit when sales are $2,000.
7. What level of sales would be required in order for the company to achieve a profit of $2,500.

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