### Part (c)
Let's complete the given tables based on the provided data for costs and income for Choc-chip delights and Caramel dreams.
#### Choc-chip delights
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline
\begin{tabular}{l}
Number of \\
units
\end{tabular} & 50 & 80 & 150 & 180 & 200 & 260 & 300 \\
\hline
Cost & 380 & 608 & 975 & 1141 & 1369 & 1521 & 1977 & 2282 \\
\hline
Income & 715 & 1144 & 1430 & 2145 & 2574 & 2860 & 3718 & 4290 \\
\hline
\end{tabular}
#### Caramel dreams
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline
\begin{tabular}{l}
Number of \\
units
\end{tabular} & 160 & 200 & 300 & 360 & 400 & 600 & 660 \\
\hline
Cost & 846 & 1057 & 1586 & 1903 & 2115 & 3172 & 3489 & 137 \\
\hline
Income & 1320 & 2112 & 2640 & 3960 & 4752 & 5280 & 6600 & 7920 \\
\hline
\end{tabular}
### Part (d)
To represent the total biscuit sales and income for the biscuit factory, we need a graph with:
- The x-axis representing the number of units sold.
- The y-axis representing the total income and cost.
- Two lines: one for total income and one for total costs.
### Part (e)
The breakeven point is where the total sales (income) equal the total costs. This can be found graphically by identifying the intersection of the income and cost lines on the graph.
### Part (f)
To determine if the factory will make a profit by selling 420 Caramel dreams and 210 Choc-chip delights, we calculate the total income and cost for these quantities and compare them:
#### Choc-chip delights
- Cost for 210 units: Interpolating between 180 (1141) and 200 (1369), the cost for 210 is approximately \[tex]$2197.
- Income for 210 units: Interpolating between 180 (2574) and 260 (2860), the income is approximately \$[/tex]3144.
#### Caramel dreams
- Cost for 420 units: Interpolating between 400 (2115) and 600 (3172), the cost for 420 is approximately \[tex]$2414.
- Income for 420 units: Interpolating between 400 (5280) and 600 (6600), the income for 420 is approximately \$[/tex]5544.
Total costs: 2197 (choc-chip) + 2414 (caramel) = \[tex]$4611.
Total income: 3144 (choc-chip) + 5544 (caramel) = \$[/tex]8688.
Since total income (\[tex]$8688) is greater than total costs (\$[/tex]4611), the factory will make a profit.
### Part (g)
To find the mark-up for both kinds of biscuits at a new price of \[tex]$15.00 each, we need to calculate the cost per unit and then the mark-up as the difference between the selling price and the cost price.
#### Choc-chip delights
- Average cost per unit = (380 + 608 + 975 + 1141 + 1369 + 1521 + 1977 + 2282) / 8 = 1274.125/8 = 159.266875.
- Selling price per unit = \$[/tex]15.00.
- Mark-up = Selling price - Cost per unit = \[tex]$15.00 - 159.266875 = -144.
#### Caramel dreams
- Average cost per unit = (846 + 1057 + 1586 + 1903 + 2115 + 3172 + 3489 + 137) / 8 = 1464.375/8 = 183.046875.
- Selling price per unit = \$[/tex]15.00.
- Mark-up = Selling price - Cost per unit = \[tex]$15.00 - 183.046875 = -168.
So, at the new price of \$[/tex]15.00, the factory will incur a loss per unit on both kinds of biscuits.
