Business Project-Chapter 7 project

You want to make money out of your house.  Pick something that you could realistically make out of your house and sell online to clients.  You are going to create two equations an equation that represents your costs with making this product and a second equation that represents your profit.  They should both be linear equations.  You need to be realistic with your numbers so take all of your expenses into account when creating that equation.  You need to set a realistic price for this item and take shipping into account as well.  After you have created these two equations you need to find their solution using substitution, elimination, graphs done on Desmos with screen shots as well as matrices solved on Desmos with screen shots.  You will then need to explain what the solution means in terms of your business and future prospects.  If you had not gotten a solution what would that have implied?  Is this business idea something worth pursuing or not?
 
STEPS

1.        What are you hoping to realistically produce?  Explain why you are able to produce this in your home now. (5 pts)    I will be producing olive oil soap. I will sell each soap for $9.99 and I will produce 180 soap bars per day. Below is the list of products and prices.

soap molds $8.99, triple butter soap base $32.00, Athena Greek olive oil $44.99, spatulas $14.99, funnel pitcher 18.99, Pyrex dish $18.27, soap cutter $29.99, scale $12.59, shipping $9.95.  
 
 
2.        Create two equations –Listing items and cost creates equations and then then create them

                Expense Equation (5 pts)

                Profit Equation (5 pts)

### **1. What are you hoping to realistically produce? Explain why you are able to produce this in your home now. (5 pts)**

I will be producing **olive oil soap** from home. I can realistically do this because I have the necessary space to make and store the soap, and I already own some of the basic equipment like soap molds, spatulas, and a soap cutter. The materials needed, such as the soap base and olive oil, can be easily purchased online. Additionally, producing 180 soap bars per day is feasible with the equipment I have, allowing me to scale production to meet demand. The soap will be sold online for **$9.99 per bar**.

### **2. Create two equations – Listing items and costs to create equations**

#### **Expense Equation (5 pts)**
Let $ x $ represent the number of soap bars produced and sold.

Here are the costs:
- **Soap molds**: $8.99 (initial cost)
- **Triple butter soap base**: $32.00 (variable cost)
- **Athena Greek olive oil**: $44.99 (variable cost)
- **Spatulas**: $14.99 (initial cost)
- **Funnel pitcher**: $18.99 (initial cost)
- **Pyrex dish**: $18.27 (initial cost)
- **Soap cutter**: $29.99 (initial cost)
- **Scale**: $12.59 (initial cost)
- **Shipping per bar**: $9.95 (variable cost per bar)

To simplify, the total initial cost is for the tools and equipment:
\[
\text{Initial Costs} = 8.99 + 14.99 + 18.99 + 18.27 + 29.99 + 12.59 = 103.82
\]

For each bar of soap, we must consider the variable costs, which include the soap base, olive oil, and shipping per bar. Let’s assume that the total variable cost per soap bar (including shipping) is calculated as follows:

- **Triple butter soap base + Olive oil per bar**: 
  - Estimation: If $32 + $44.99 = $76.99 for materials yields 180 bars, the material cost per bar is $ \frac{76.99}{180} \approx 0.43 $ dollars.
  - Shipping cost: $9.95 per bar.

Thus, the total cost per bar is:

\[
\text{Cost per bar} = 0.43 + 9.95 = 10.38 \, \text{dollars}
\]

So, the **expense equation** becomes:

\[
\text{Total Expense} = 10.38x + 103.82
\]

Where $ x $ represents the number of soap bars produced and sold.

#### **Profit Equation (5 pts)**
The profit for each soap bar is calculated as:

\[
\text{Profit per bar} = \text{Selling Price} - \text{Cost per bar} = 9.99 - 10.38 = -0.39
\]

Thus, the **profit equation** becomes:

\[
\text{Total Profit} = (-0.39x) - 103.82
\]

This indicates a loss on each bar initially. However, increasing the selling price or reducing the shipping costs could improve profitability.

---

Would you like help solving these equations using substitution or elimination, or do you want more details on the break-even point? Let me know if you want a graph or matrix solution using Desmos as well.

Here are five related questions to expand on this:
1. How could you reduce your shipping costs to improve profit margins?
2. What price should you set to ensure you make a profit on each soap bar?
3. What would be your total cost for 500 soap bars?
4. If you could increase your daily production, how would that impact your break-even point?
5. How would offering discounts for bulk orders affect your profitability?

**Tip:** Keep track of both variable and fixed costs, as variable costs directly influence your profit per unit.

Explore the cost and profit analysis for producing olive oil soap from home. Learn how to create expense and profit equations, calculate variable and fixed costs, and analyze profit margins. Suitable for adult learners interested in home-based business economics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation