Unit VII Assignment: Break-Even Analysis Uses Two ✓ Solved

Unit Vii Assignment Breaking Evenbreakeven Analysis Uses Two Function

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.

Imagine that you are a 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.

Sample Paper For Above instruction

1. Item Description

The item I will produce and sell in my store is a handcrafted ceramic mug. This product is popular among consumers who appreciate artisanal and unique homeware pieces. The handcrafted ceramic mug offers a personal touch and a distinct design that differentiates it from mass-produced alternatives.

2. Cost to Produce

The cost of materials and labor to produce one ceramic mug is estimated at $20. This includes clay, glazes, brushes, and the time spent by artisans to craft each mug.

3. Selling Price

I will sell each ceramic mug for $45. The selling price is higher than the production cost to ensure profitability and cover additional expenses such as marketing, packaging, and store rent.

4. Cost Function, C(x)

The fixed cost is $5,000, and the variable cost per mug is $20. Using the formula for the cost function:

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

C(x) = 5000 + 20x

5. Revenue Function, R(x)

The selling price per mug is $45. Therefore, the revenue function is:

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

R(x) = 45x

6. System of Equations

To find the breakeven point, we set cost and revenue equal:

  • Y = C(x) = 5000 + 20x
  • Y = R(x) = 45x

7. Solving the System for Breakeven Point

Set the equations equal to each other:

5000 + 20x = 45x

Subtract 20x from both sides:

5000 = 25x

Divide both sides by 25:

x = 200

The breakeven quantity is 200 mugs.

Calculate the total revenue at this point:

R(200) = 45 × 200 = $9,000

Calculate the total cost at this point:

C(200) = 5000 + 20 × 200 = 5000 + 4000 = $9,000

Thus, at 200 mugs, revenue equals cost, confirming the breakeven point.

8. Number of Items to Sell and Produce to Break Even

You must sell and produce 200 mugs to break even.

9. Meaning of the Y-coordinate of the Breakeven Point

The y-coordinate represents the total revenue or total cost at the breakeven point, which is $9,000. It is the point where income equals expense, indicating no profit or loss.

10. Items Needed to Make a Profit of $2,500

First, define profit function P(x):

  • P(x) = R(x) – C(x)

Substitute the functions:

P(x) = 45x – (5000 + 20x) = 45x – 5000 – 20x = 25x – 5000

Set profit to $2,500 and solve for x:

25x – 5000 = 2500

Add 5000 to both sides:

25x = 7500

Divide both sides by 25:

x = 300

Answer: You need to sell and produce at least 300 mugs to make a profit of $2,500.

References

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