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 form $1,000 to $4,000, their costs increased from $750 to $1,500.

a. Which is the dependent variable and which is the independent variable? Explain.

b. Assuming that a linear functional relationship exists, determine the equation that relates total costs to total sales.

c. 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.

d. Explain why the nature of the relationship may change if sales exceed $5,000.

e. Find and interpret C(2,000).

f. Calculate the profit when sales are $2,000.

g. What level of sales would be required in order for the company to achieve a profit of $2,500.