Answer :
### 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.
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.
