### 1.1.1 Write down a formula to represent Chloe's total expenses:
To determine Chloe's total expenses, we need to include both the fixed cost of renting the stall and the variable cost of making the tortillas.
Let:
- [tex]\( E \)[/tex] be the total expenses.
- [tex]\( R \)[/tex] be the fixed rental cost for the stall, which is R500.
- [tex]\( S \)[/tex] be the cost to make one tortilla.
- [tex]\( n \)[/tex] be the number of tortillas sold.
The formula for total expenses [tex]\( E \)[/tex] can be written as:
[tex]\[ E = R + nS \][/tex]
Given [tex]\( R = 500 \)[/tex]:
[tex]\[ E = 500 + nS \][/tex]
### 1.1.2 Draw up a table to represent Chloe's expenses if she sells [tex]\( 0, 50, 100, 150, 200, \)[/tex] and [tex]\( 250 \)[/tex] tortillas:
Using the expense formula [tex]\( E = 500 + nS \)[/tex] and assuming [tex]\( S \)[/tex] (the cost to make one tortilla) is R5:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Number of tortillas} & \text{Total expenses (R)} \\
\hline
0 & 500 \\
50 & 750 \\
100 & 1000 \\
150 & 1250 \\
200 & 1500 \\
250 & 1750 \\
\hline
\end{array}
\][/tex]
### 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.
To plot the graphs:
1. Axes Setup:
- X-axis: Number of tortillas sold [tex]\((n)\)[/tex].
- Y-axis: Rand (R).
2. Total Income Line:
- Coordinates based on the given table:
[tex]\[
(0, 0), (50, 750), (100, 1500), (150, 2250), (200, 3000), (250, 3750)
\][/tex]
3. Total Expenses Line:
- Coordinates based on the calculated expenses:
[tex]\[
(0, 500), (50, 750), (100, 1000), (150, 1250), (200, 1500), (250, 1750)
\][/tex]
4. Plotting both lines:
- Income line:
[tex]\[
\text{Straight line passing through points } (0, 0), (50, 750), (100, 1500), (150, 2250), (200, 3000), (250, 3750)
\][/tex]
- Expenses line:
[tex]\[
\text{Straight line passing through points } (0, 500), (50, 750), (100, 1000), (150, 1250), (200, 1500), (250, 1750)
\][/tex]
Ensure to clearly mark and label the axes, the lines for income and expenses, and any intersection points.
### 1.1.4 Determine the minimum number of tortillas that Chloe must sell in order to break even:
To break even, Chloe's income must equal her expenses.
From the lines of income [tex]\([0, 750, 1500, 2250, 3000, 3750]\)[/tex] and expenses [tex]\([500, 750, 1000, 1250, 1500, 1750]\)[/tex], we identify the first point where income meets or exceeds expenses:
- Break-even occurs at 50 tortillas sold, where both income and expenses are 750.
Thus, Chloe must sell a minimum of 50 tortillas to break even.
