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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:
[tex]\[ \text{Total Expenses} = \cdots \][/tex]

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 Sale of 240 tortillas & & Fixed cost & \\
\hline & & Cost of each tortilla & \\
\hline Total Income & & Total Cost of 240 tortillas & \\
\hline & & Profit & \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's go through each part of the question step by step.

### 1.1.1 Formula to represent Chloe's total expenses:

To find out Chloe's total expenses, we need to consider both the fixed cost (rent for the stall) and the variable cost (cost per tortilla).

Let's denote:
- Fixed cost as [tex]\( F \)[/tex],
- Cost per tortilla as [tex]\( c \)[/tex],
- Number of tortillas as [tex]\( n \)[/tex].

Chloe's total expenses formula can be written as:

[tex]\[ \text{Total Expenses} = F + (c \times n) \][/tex]

Here:
- [tex]\( F = 500 \)[/tex] R (the rent for the stall),
- [tex]\( c = 5 \)[/tex] R (cost to make one tortilla).

So, the formula becomes:

[tex]\[ \text{Total Expenses} = 500 + (5 \times n) \][/tex]

### 1.1.2 Table of Chloe's expenses:

Let's calculate Chloe's expenses for selling 0, 50, 100, 150, 200, and 250 tortillas and create a table.

[tex]\[ \begin{array}{|l|c|c|c|c|c|c|} \hline \text{Number of tortillas} & 0 & 50 & 100 & 150 & 200 & 250 \\ \hline \text{Total Expenses (R)} & 500 & 750 & 1000 & 1250 & 1500 & 1750 \\ \hline \end{array} \][/tex]

### 1.1.3 Drawing the line graphs:

On the same set of axes, draw the following lines:
- Total Income vs. Number of Tortillas:
- From the given data, Total Income = [tex]\( 15 \times \text{Number of tortillas} \)[/tex].

- Total Expenses vs. Number of Tortillas:
- From the given data, Total Expenses = [tex]\( 500 + 5 \times \text{Number of tortillas} \)[/tex].

Plot the points from the tables provided for both the Total Income and Total Expenses on the graph, and connect them to form lines. Ensure to label the graphs accordingly.

### 1.1.4 Minimum number of tortillas to break even:

To determine the break-even point, where Total Income equals Total Expenses, we need to solve the following equation:
[tex]\[ \text{Total Income} = \text{Total Expenses} \][/tex]

Using the formulas:
[tex]\[ 15n = 500 + 5n \][/tex]

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

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

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

### 1.1.5 Income and expense statement for 240 tortillas:

Chloe's profit can be calculated by first determining her total income and total expenses for selling 240 tortillas:

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

- Total Expenses:
Let's use the expenses formula:
[tex]\[ \text{Total Expenses} = 500 + (5 \times 240) = 500 + 1200 = 1700 \, \text{R} \][/tex]

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

So, we can fill in the income and expense statement as follows:

[tex]\[ \begin{array}{|l|l|l|l|} \hline \multicolumn{2}{|c|}{\text{Income}} & \multicolumn{2}{c|}{\text{Expense}} \\ \hline \begin{array}{l} \text{Sale of} \\ \text{240 tortillas} \end{array} & 3600 \, \text{R} & \text{Fixed cost} & 500 \, \text{R} \\ \hline && \begin{array}{l} \text{Cost of each} \\ \text{tortilla} \end{array} & 5 \, \text{R} \\ \hline \text{Total Income} & 3600 \, \text{R} & \text{Total Cost of 240 tortillas} & 1700 \, \text{R} \\ \hline && \text{Profit} & 1900 \, \text{R} \\ \hline \end{array} \][/tex]

This completes the detailed, step-by-step solution for the given question.

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