College Algebra Discussion Solutions
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.
1. Briefly explain one item that you will be producing and selling in your store.
2. 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 =
3. 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 =
4. 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)
5. 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)
6. 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)
7. 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.
8. How many items must you sell and produce in order to break even?
9. 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.
10. 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.
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