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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.



Answer :

GinnyAnswer
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 are comprised of:
1. A fixed cost of R500 for renting the stall.
2. A variable cost of R5 for each tortilla she makes.

We can write the total expenses ([tex]\(E\)[/tex]) as a function of the number of tortillas ([tex]\(n\)[/tex]) she makes:
[tex]\[ \text{Total Expenses} = 5n + 500 \][/tex]

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

[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Expenses (R)} \\ \hline 0 & 5(0) + 500 = 500 \\ 50 & 5(50) + 500 = 250 + 500 = 750 \\ 100 & 5(100) + 500 = 500 + 500 = 1000 \\ 150 & 5(150) + 500 = 750 + 500 = 1250 \\ 200 & 5(200) + 500 = 1000 + 500 = 1500 \\ 250 & 5(250) + 500 = 1250 + 500 = 1750 \\ \hline \end{array} \][/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 draw the line graph, we plot the number of tortillas on the x-axis and the amount in Rands on the y-axis.

Plot the Total Income Line:
The total income ([tex]\(I\)[/tex]) can be determined using the formula:
[tex]\[ I = 15n \][/tex]

Using the given table of incomes:
[tex]\[ \begin{array}{|c|c|} \hline \text{Number of tortillas} & \text{Total Income (R)} \\ \hline 0 & 0 \\ 50 & 750 \\ 100 & 1500 \\ 150 & 2250 \\ 200 & 3000 \\ 250 & 3750 \\ \hline \end{array} \][/tex]

Plot the Total Expenses Line:
Using the table of expenses calculated in 1.1.2:
[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]

Drawing the Graph:
1. Draw the x-axis and y-axis.
2. Plot the points for total income and total expenses.
3. Draw one line connecting the points for total income.
4. Draw another line connecting the points for total expenses.
5. Label each line accordingly.

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

To find the break-even point, we need to set the total income equal to the total expenses and solve for [tex]\(n\)[/tex]:

[tex]\[ 15n = 5n + 500 \][/tex]

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

[tex]\[ 10n = 500 \][/tex]

Divide both sides by 10:

[tex]\[ n = 50 \][/tex]

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

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