# Sanders Unit VII MAT 1302 Assignment

**Unit VII Assignment: Breaking Even**

Breakeven analysis uses two functions to describe the revenue and cost of a particular product. The breakeven point is the number of products that a business must produce and sell so that the money coming in is equal to the money going out. In this assignment, you will be asked to create a system of equations based on the cost and revenue of a particular business. You will solve the system to determine the business’s breakeven point.

**Instructions:** Imagine that you are business owner who produced a particular item to sell in your new store. Answer questions 1–10. Save all of your work to this template and submit it in Blackboard for grading.

- Briefly explain one item that you will be producing and selling in your store.
- How much does the item cost you to produce? Consider the cost of materials and labor. Select an amount between $1 and $50. Round to the nearest dollar.

Cost per item produced = | $ |

- How much will you sell the product for? Select an amount between $1 and $100. The sold price must be more than what it costs to produce the item. Round to the nearest dollar.

Price per unit sold = | $ |

- Write the cost function, C(x), of producing x amount of items. Assume that you have a
**fixed cost $5,000**. Replace the “?” with the appropriate numbers.

C(x) = fixed cost + (cost per item produced)(x)

C(x) = ? + (?)(x)

- Write the revenue function, R(x), from the sale of x items. Replace the “?” with the appropriate numbers.

R(x) = (price per item sold)(x)

R(x) = (?)(x)

- Replace C(x) and R(x) with y. This means that the cost and revenue will be the same. Write the system of equations below.

Y = write equation found for C(x)

Y = write equation found for R(x)

- Use the
**substitution method**to solve the system of equations found in question 6. The solution is the breakeven point. Show each step of your work below. Round your final answer for x to the nearest whole number and use the rounded value of x to solve for y. Round y to the nearest cent or to two decimal places. - How many items must you sell and produce in order to break even?
- What does break-even mean? In your own words, include what the x and y-coordinates of the break-even point mean in your definition. You should not restate the coordinates you found above.
- How many items will you need to sell in order to make a profit of $2,500? Round up to the nearest whole number.

First, find P(x). To do this, substitute the expressions for R(x) and C(x) found in questions 4 and 5 into the equation below and simplify.

P(x) = R(x) – C(x)

Next, replace P(x) with 2500 into the equation above and solve for x. Round up to the nearest whole number. Show your work below.

Answer: You need to sell ____ items in order to make a profit of $2,500.