QUESTION 1

A food fair is going to be held at Zoo Lake. Chloe decides to set up a stall selling tortillas. It costs Chloe R5 to make a tortilla and R500 to rent the stall. She sells each tortilla for R15.

The table below shows the income that Chloe will make if she sells the tortillas:

\begin{tabular}{|l|c|c|c|c|c|c|}
\hline Number of tortillas & 0 & 50 & 100 & 150 & 200 & 250 \\
\hline Total Income (R) & 0 & 750 & 1500 & 2250 & 3000 & 3750 \\
\hline
\end{tabular}

1.1.1 Write down a formula to represent Chloe's total expenses:

Total Expenses = ...

1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas.

1.1.3 Use Annexure A to draw, on the same set of axes, a line graph representing Chloe's total income and another line representing her expenses. Label the graphs accordingly.

1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even.

1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement on the ANNEXURE PROVIDED for the sale of 240 tortillas and show how much profit she made.

\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{Income} & \multicolumn{2}{|c|}{Expense} \\
\hline \begin{tabular}{l}
Sale of \\
240 tortillas
\end{tabular} & & Fixed cost & \\
\hline & & \begin{tabular}{l}
Cost of each \\
tortilla
\end{tabular} & \\
\hline Total Income & & Total Cost of 240 tortillas & \\
\hline & & Profit & \\
\hline
\end{tabular}



Answer :

Alright, let's go through each part of the question step-by-step:

### 1.1.1 Write down a formula to represent Chloe's total expenses:
Chloe's total expenses comprise a fixed cost of R500 for renting the stall, plus an additional variable cost of R5 for each tortilla she makes. Therefore, the formula to represent Chloe's total expenses ([tex]\(E\)[/tex]) when she sells [tex]\(n\)[/tex] tortillas is:
[tex]\[ \text{Total Expenses} = 500 + 5n \][/tex]

### 1.1.2 Draw up a table to represent Chloe's expenses if she sells 0, 50, 100, 150, 200, and 250 tortillas:
Use the formula from 1.1.1 to calculate the expenses for each number of tortillas.

| Number of tortillas | Total Expenses (R) |
|---------------------|--------------------|
| 0 | 500 |
| 50 | 750 |
| 100 | 1000 |
| 150 | 1250 |
| 200 | 1500 |
| 250 | 1750 |

### 1.1.3 Draw a Line Graph:
On the provided annexure:
- Plot the total income for different numbers of tortillas using the given table:
- Income when selling [tex]\( n \)[/tex] tortillas: [tex]\( \text{Total Income} = 15n \)[/tex]
- Use the table values: (0, 0), (50, 750), (100, 1500), (150, 2250), (200, 3000), (250, 3750)

- Plot the total expenses using the table calculated in 1.1.2:
- Expenses when selling [tex]\( n \)[/tex] tortillas: [tex]\( \text{Total Expenses} = 500 + 5n \)[/tex]
- Use the table values: (0, 500), (50, 750), (100, 1000), (150, 1250), (200, 1500), (250, 1750)

Draw these points and connect them with lines, clearly labeling the graphs as "Total Income" and "Total Expenses."

### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even:
- Break-even occurs when total income equals total expenses:
[tex]\[ 15n = 500 + 5n \][/tex]

Subtract 5n from both sides:
[tex]\[ 10n = 500 \][/tex]

Divide by 10:
[tex]\[ n = 50 \][/tex]

Therefore, Chloe must sell at least 50 tortillas to break even.

### 1.1.5 Chloe sold 240 tortillas. Complete the income and expense statement for the sale of 240 tortillas and calculate the profit:

Income:

- Sale of 240 tortillas:
[tex]\[ \text{Total Income} = 240 \times 15 = 3600 \text{R} \][/tex]

Expenses:

- Fixed cost for renting the stall: 500 R
- Cost of each tortilla ([tex]\(5 \text{R} \times 240\)[/tex]):
[tex]\[ \text{Total Cost of 240 tortillas} = 240 \times 5 = 1200 \text{R} \][/tex]

Add the fixed cost to the variable cost:
[tex]\[ \text{Total Expenses} = 500 + 1200 = 1700 \text{R} \][/tex]

Profit:

- Profit is calculated as:
[tex]\[ \text{Profit} = \text{Total Income} - \text{Total Expenses} \][/tex]
[tex]\[ \text{Profit} = 3600 - 1700 = 1900 \text{R} \][/tex]

So, Chloe's income and expense statement for selling 240 tortillas is as follows:

| | Income (R) | Expense (R) |
|---------------|------------|-------------|
| Sale of 240 tortillas | 3600 | Fixed cost: 500 |
| | | Cost of each tortilla: 1200 |
| Total Income | 3600 | Total Cost of 240 tortillas: 1700 |
| | | Profit: 1900 |

Chloe made a profit of R1900 from selling 240 tortillas.