# Linear Equations

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.

https://brainmass.com/economics/output-and-costs/linear-equations-retailing-operation-276023

#### Solution Preview

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 ...

#### Solution Summary

Linear equations in a retailing operations are determined. A complete, neat and step-by-step solution is provided in the attached Excel file.