Erie Community College
Title III
Algebra Assignment
Interdisciplinary Course Materials
Business Administration
Courses: MT007, MT013
Course Outline Topics: Systems of Linear Equations
Title: How Much is that Doggie in the Window?
Project description: The student will learn about Breakeven Points when working with a system of equations that involve cost equations and revenue equations.
Things to Learn Before Starting the Project: How to solve systems of equations by graphing and at least one algebraic method.
Author: Justinger (Mathematics)
Curriculum Experts: Brennan (Business Administration Fernbach (English)
Semester Created: Spring 2008
Contents:
I Project Sheet with explanations of business terms dealing with the breakeven point.
II Student Project Sheet
III Grading Suggestion.
IV Project Extensions
I. Breakeven Analysis and Operating Leverage
Breakeven Analysis (or cost/volume/profit analysis) is a linear analysis used by business people for financial analysis in determining what sales volume a business needs to generate before making a profit on a project. It is a very important tool when developing a pricing strategy as part of a marketing or business plan.
Operating Leverage refers to degree to which the firm produces it product with a fixed cost versus variable cost commitment. For example, the higher the fixed cost, the lower the variable cost, therefore, the higher the degree of operating leverage. Generally speaking, a firm generates a greater amount of profit past breakeven volume the higher its operating leverage. It also generates a greater loss with high operating leverage if it doesn’t achieve the breakeven volume.
To conduct a breakeven analysis you need the following information.
A. Cost Structure for the Project
Virtually all of your business's costs will fall, more or less neatly, into one of two categories:
· Variable costs, which increase directly in proportion to the level of sales in dollars or units sold. Depending on your type of business, some examples would be cost of goods sold, sales commissions, shipping charges, delivery charges, costs of direct materials or supplies, wages of part-time or temporary employees, and sales or production bonuses.
· Fixed costs, which remain the same regardless of your level of sales. Depending on your type of business, some typical examples would be rent, interest on debt, insurance
Total Cost equals the addition of both variable and fixed costs at each level of sales
B. Sales Revenue for the Project
Once price is determined then sales revenue can be calculated for each number of units sold.
C. Breakeven Volume (Point)
The breakeven volume (point) is determined by finding the point where Total Revenue equals Total Costs. Every price and volume below breakeven will result in a loss if the sales volume is not reached. Every price and volume above breakeven will result in a profit if the sales volume is reached
When the breakeven point is determined, the businessperson must address a series of questions such as:
1. Is it realistic to achieve breakeven at the established price?
2. It not, should price be adjusted? Up?, Down?
3. Is it possible to adjust costs? Up?, Down?
4. What concerns must be addressed when adjusting costs?, price?
a. Union contracts
b. Competition
c. Government regulations (anti trust laws)
d. Substitution of fixed for variable costs and vice versa.
e. Ability to influence cost components
f. Elasticity factors of demand
How Much is that Doggie in the Window?
Name: ________________________________
You won a ceramics studio/ shop. You make puppy statues to sell. You have come up with some formulas to help you find the breakeven point for the number of puppies that you should produce per week. X represents the number of puppy statues.
Cost of puppies = variable cost of producing a puppy statue times number of puppy statues produced (X) plus a fixed cost of $2,000 for the costs of your business
Revenue = price puppy statues are sold for times number of puppy statues sold (X)
It costs (variable) you $4.72 to produce a puppy statue. Use the internet (something like eBay) to estimate the price of a puppy statue (you pick the breed) that is of good quality and stands about 10 to 12 inches tall. Use this information to complete your equations.
Your equations are:
Cost = ______________ X + 2000
Revenue = ______________X
Graph both equations on the same set of axis.
At what point do the lines cross? ________________________
Interpret your results:
Solve the system of equations by an algebraic method in the space below.
What is the number of statues you must produce next week to breakeven? __________________
What would be your revenue for this level of production? ______________________________
Profit equals revenue minus costs.
What is your profit for this level of production? _____________________________________
In the past you have seen that you can produce a maximum of 500 statues a week. Generally your distribution company can sell 300 to 400 statues a week.
Is the scenario you created above possible within the constraints you have from past weeks? ___________
If no, should the price be adjusted, up or down? Explain:
Grading Suggestions
Completing Equations 20%
Graphing Equations 25%
Algebraic Solution 25%
Interpretation of results 30%
Project Extensions
1. Research other areas of business that use systems of equations to help solve problems.
2. Discuss maximizing profit and minimizing cost.
3. Have students do an Internet search to find other areas that use systems of equations to solve problems.
Erie community College
Title III Grant