Algebra I Break-Even Analysis Introduction: Application of Linear Systems of Equations Answer the following questions:

Transcription

1 Algebra I Break-Even Analysis Introduction: Application of Linear Systems of Equations Answer the following questions: 1. What are the two main types of business costs? 2. What is the definition of break-even point for a business? 3. What are variable costs? 4. What are fixed costs? 5. Why might it be important for a business to calculate break-even point? 6. What is net income? 7. What is a net loss? 8. What is a net gain? 9. What is a unit cost?

2 10. What is profit? 11. What are sales? 12. What are total fixed costs? EXAMPLES OF FIXED COSTS EXAMPLES OF VARIABLE COSTS Review: Solving a System of Equations What is the solution of the following systems? y = 40x y = 10x + 0 y = 52x + 0 y = 4x + 12 Example 1: a. Matthew buys M&M s at Costco for $19.20 for a box of 48. What is the unit cost for each package of M&M s? b. If he sells them for $.60 per package, how much money is he making on each package? What did you do to get this answer? c. How many packages will he need to sell in order to get his original investment back if he sells them for $.60 per package?

3 Example 2: Travis and his band are planning to record their first CD. The initial start-up costs is $1,500 and each CD will cost $4 to produce. They plan to sell their CDs for $10 each. How many CDs must the band sell before they make a profit? Steps: Let x = Let y = Cost Equation: Cost of x CDs is cost per CD plus the startup cost. Income Equation: Income from x CDs is price per CD times the number of CDs sold. Example 3: A hot dog vendor at a local baseball park has the following fixed costs: - $25 license - $100 for equipment The variable costs are estimated to be $50 for twelve dozen (or 144) hot dogs and buns as well as condiments and paper products. The hot dogs will sell for $1.50 each. How many hot dogs will the vendor need to sell in order to break even? Example 4: a. You are planning a dance. Let us make a list of items for our dance that are fixed and variable: Fixed Cost Variable Costs Rent for the Food and Drinks space $25.00 $2.00 DJ for the music - Glow Sticks $75.00 $1.00 Advertising $15.00 Supplies $5.00 Total = Total = Selling price is $8.00 per ticket. Now that we know our fixed costs, variable costs, and ticket price, we can determine how many tickets need to be sold before we start earning money. How many tickets would you have to sell in order to break even?

4 Example 5: What is the break-even point in units for a business whose total fixed costs are $275,450; selling price per unit is $16; and variable cost per unit is $14.75? Example 6: Token Metal Products, Inc., manufactures can openers. Each can opener costs $0.19 to make and can be sold for $0.44 each. The company has fixed costs of $142,570 for rent, equipment and salaries. How many can openers must be sold for Token Metal Products, Inc., to break-even? To make a profit? Example 7: You plan on starting a lawn mowing business. It is going to cost you $450 for a new lawn mower, and approximately $2.50 per lawn for gas, bags, and oil. You plan to charge $15 per lawn. How many lawns must you mow to break-even? What is the amount of income and expenses at the break-even point? Example 8: Central Publishing Company plans to produce do-it-yourself books to be sold at $14.95 each. It costs the company $10.43 to produce each copy of a book, and $180,800 for the machines and labor. How many books need to be sold for the company to break even? Example 9: Toys R Us produces toy dump trucks. Each toy costs $4.00 to make and can be sold for $12 each. The company has fixed costs of $203,000 for rent, equipment, and salaries. How many trucks need to be sold to break even?

5 Example 10: Chrysler has developed a new minivan that has a start up cost of $ 45,000,000. Each new van costs $ 18,000 to make. If Chrysler plans to sell the minivans for $ 30,000, how many do they have to sell to break even? Example 11: A small fast food restaurant invests $5,000 to produce a new food item that will sell for $3.49 each. Each item can be produced for $2.16. How many items must be sold to break even? Example 12: A company that manufactures bicycles has a fixed cost of $100,000. It costs $100 to produce each bicycle. The selling price per bike is $300. How many bikes do they need to sell to break even? Example 13: The following information is given for a company that produces collectable dolls. How many dolls do they need to sell to break even? Selling Price per unit $ 17 Fixed Costs Selling & Administrative $ 130,000 Interest Expense $ 10,000 Variable Costs Cost of Goods Sold $ 4 Selling & Administrative $ 3 Example 14: Healthy Foods, Inc., sells 50-pound bags of grapes to the military for $10 a bag. Their rent and salaried employees costs the company $80,000, while the variable costs of the grapes are $.10 per pound. A.What is the break-even point in bags?