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Shelly manufactures cute bags in her spare time. She decides to sell her product at the Willow Dam Sunday Market. To rent a stall at the market costs R80.00 per day. The production cost of a bag is [tex]$R 75.00$[/tex]. Shelly wants to sell her bags at R100.00 each.

2.1 What is Shelley's selling price for one bag?

2.2 What is Shelley's cost price for one bag?

2.3 Identify Shelley's fixed costs.

2.4 Complete the following tables for income and costs for Shelley's business:

Expenses:
Income:

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\end{tabular}

2.5 Use the information provided in the tables to draw line graphs for costs and income on the set of axes provided below. Label your graphs appropriately.

2.6 What is the point of intersection of the graphs called?

2.7 Explain what is meant by this point of intersection.

2.8 How many bags must Shelly sell to start showing a profit?

2.9 Calculate the amount of profit on 17 bags. Show all your calculations.

Income and expenses for Shelley's bags:
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\end{tabular}



Answer :

GinnyAnswer
Let's tackle each part of the problem step by step.

### 2.1 Shelley's Selling Price for One Bag:
Shelley's selling price for one bag is R100.00.

### 2.2 Shelley's Cost Price for One Bag:
Shelley's cost price for one bag is R75.00.

### 2.3 Shelley's Fixed Costs:
Shelley's fixed costs, which is the cost to rent a stall at the market per day, is R80.00.

### 2.4 Income and Costs for Shelley's Business:
To complete the tables, let's use the provided data:
- Selling price (Income) per bag: R100.00
- Cost price per bag: R75.00
- Fixed costs to rent the stall: R80.00 per day

Income Table:
| Number of Bags Sold | Total Income (R) |
|---------------------|------------------|
| 1 | 100 |
| 2 | 200 |
| 3 | 300 |
| 4 | 400 |
| 5 | 500 |
| ... | ... |

Cost Table:
| Number of Bags Made/Sold | Total Cost (R) |
|--------------------------|----------------|
| 1 | 155 |
| 2 | 230 |
| 3 | 305 |
| 4 | 380 |
| 5 | 455 |
| ... | ... |

Explanation:
- Total Income is calculated as: Selling Price per Bag × Number of Bags Sold
- Total Cost is calculated as: Fixed Costs + (Cost Price per Bag × Number of Bags Made/Sold)

### 2.5 Line Graphs for Costs and Income:
To draw parallel line graphs for Costs and Income, plot 'Number of Bags Sold' on the x-axis and both 'Total Income' and 'Total Costs' on the y-axis.

### 2.6 Point of Intersection:
The point of intersection of these graphs is called the break-even point.

### 2.7 Explanation of the Point of Intersection:
The break-even point is where the total income equals the total costs. At this point, Shelly does not make any profit but also does not incur any loss.

### 2.8 Number of Bags Shelly Must Sell to Start Showing a Profit:
Shelly needs to sell 4 bags to start showing a profit. Calculations:
[tex]\[ \left(\text{Fixed Costs} / (\text{Selling Price per Bag} - \text{Cost Price per Bag})\right) = 80 / (100 - 75) = 80 / 25 = 3.2 \][/tex]
Since Shelly cannot sell a fraction of a bag, we round up to the next whole number.
Thus, Shelly must sell 4 bags.

### 2.9 Calculate the Amount of Profit on 17 Bags:
To calculate the profit:

1. Total Income for 17 bags:
[tex]\[ \text{Total Income} = 17 \times 100 = R1700 \][/tex]

2. Total Costs for 17 bags:
[tex]\[ \text{Total Costs} = 80 + (17 \times 75) = 80 + 1275 = R1355 \][/tex]

3. Profit:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Costs} \][/tex]
[tex]\[ \text{Profit} = 1700 - 1355 = R345 \][/tex]
So, the amount of profit on 17 bags is R345.

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