Answer :
Let's go through the entire problem step-by-step.
### 3.1 Explain the meaning of the word cost price.
Cost price refers to the total amount that has been spent to produce a product. It includes all the expenses that are incurred in making a product ready for sale, such as raw materials, labor, and overhead costs.
---
### 3.2 Now calculate the values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex].
#### Calculating [tex]\( A \)[/tex]:
[tex]\( A \)[/tex] is the cost of 0.04 kg of coffee.
Given that 1 kg of coffee costs R97.95, we find [tex]\( A \)[/tex] using the proportion:
[tex]\[ A = 0.04 \, \text{kg} \times \text{R} 97.95 / \, \text{kg} = \text{R} 3.918 \][/tex]
#### Calculating [tex]\( B \)[/tex]:
[tex]\( B \)[/tex] is the amount of milk per cup in terms of cost. Given that 1 L of milk costs R11.99 and each cup uses R1.20 worth of milk, we calculate [tex]\( B \)[/tex] as follows:
[tex]\[ B = \text{R} 1.20 / \text{R} 11.99 \approx 0.1000834028356964 \, \text{L} \][/tex]
#### Calculating [tex]\( C \)[/tex]:
[tex]\( C \)[/tex] is the total cost per cup of coffee. This includes the cost of coffee, milk, sugar, foam cups, and spoons. Given the breakdown:
- Coffee: R3.918
- Milk: R1.20
- Sugar: R0.13
- Foam cups: R1.78
- Spoons: R0.26
So, the total cost per cup ( [tex]\( C \)[/tex] ) is:
[tex]\[ C = \text{R} 3.918 + \text{R} 1.20 + \text{R} 0.13 + \text{R} 1.78 + \text{R} 0.26 = \text{R} 7.288 \][/tex]
---
### 3.3 Determine the selling price of one cup of coffee if she wants to have a profit margin of 25%.
To determine the selling price with a 25% profit margin, we use the formula for selling price [tex]\( S \)[/tex]:
[tex]\[ S = C \times (1 + \text{Profit Margin}) \][/tex]
Where [tex]\( C = \text{R} 7.288 \)[/tex] and the profit margin is 0.25 (25%):
[tex]\[ S = \text{R} 7.288 \times (1 + 0.25) = \text{R} 7.288 \times 1.25 = \text{R} 9.11 \][/tex]
So, the selling price should be R9.11 per cup.
---
### 3.4 Determine Mary's fixed costs per day.
Mary's fixed costs per day include the stall cost and the travel cost:
[tex]\[ \text{Fixed Costs} = \text{R} 40 + \text{R} 14.20 = \text{R} 54.20 \][/tex]
---
### 3.5 Provide an equation for the expenses of selling coffee per day.
Let the number of cups of coffee sold per day be denoted as [tex]\( x \)[/tex].
The total expense per day [tex]\( E(x) \)[/tex] includes the fixed costs and the variable cost per cup of coffee. The variable cost per cup is [tex]\( C = \text{R} 7.288 \)[/tex]:
[tex]\[ E(x) = \text{Fixed Costs} + \text{(Cost per cup)} \times \text{(Number of cups sold)} \][/tex]
[tex]\[ E(x) = \text{R} 54.20 + \text{R} 7.288 \times x \][/tex]
---
### 3.6 Mary decides to sell the coffee at R10,00 per cup.
At this point, since the graph is not provided, we cannot directly reference it. However, generally, from the income and expenses graphs, you would be able to determine the break-even point, profit, and loss based on the number of cups sold.
Knowing that the selling price is R10.00 per cup, you can set up the income equation:
[tex]\[ \text{Income}(x) = \text{Selling Price} \times x \][/tex]
[tex]\[ \text{Income}(x) = \text{R} 10.00 \times x \][/tex]
You can then compare the income and expense equations to determine profitability and other financial metrics.
### 3.1 Explain the meaning of the word cost price.
Cost price refers to the total amount that has been spent to produce a product. It includes all the expenses that are incurred in making a product ready for sale, such as raw materials, labor, and overhead costs.
---
### 3.2 Now calculate the values [tex]\( A \)[/tex], [tex]\( B \)[/tex], and [tex]\( C \)[/tex].
#### Calculating [tex]\( A \)[/tex]:
[tex]\( A \)[/tex] is the cost of 0.04 kg of coffee.
Given that 1 kg of coffee costs R97.95, we find [tex]\( A \)[/tex] using the proportion:
[tex]\[ A = 0.04 \, \text{kg} \times \text{R} 97.95 / \, \text{kg} = \text{R} 3.918 \][/tex]
#### Calculating [tex]\( B \)[/tex]:
[tex]\( B \)[/tex] is the amount of milk per cup in terms of cost. Given that 1 L of milk costs R11.99 and each cup uses R1.20 worth of milk, we calculate [tex]\( B \)[/tex] as follows:
[tex]\[ B = \text{R} 1.20 / \text{R} 11.99 \approx 0.1000834028356964 \, \text{L} \][/tex]
#### Calculating [tex]\( C \)[/tex]:
[tex]\( C \)[/tex] is the total cost per cup of coffee. This includes the cost of coffee, milk, sugar, foam cups, and spoons. Given the breakdown:
- Coffee: R3.918
- Milk: R1.20
- Sugar: R0.13
- Foam cups: R1.78
- Spoons: R0.26
So, the total cost per cup ( [tex]\( C \)[/tex] ) is:
[tex]\[ C = \text{R} 3.918 + \text{R} 1.20 + \text{R} 0.13 + \text{R} 1.78 + \text{R} 0.26 = \text{R} 7.288 \][/tex]
---
### 3.3 Determine the selling price of one cup of coffee if she wants to have a profit margin of 25%.
To determine the selling price with a 25% profit margin, we use the formula for selling price [tex]\( S \)[/tex]:
[tex]\[ S = C \times (1 + \text{Profit Margin}) \][/tex]
Where [tex]\( C = \text{R} 7.288 \)[/tex] and the profit margin is 0.25 (25%):
[tex]\[ S = \text{R} 7.288 \times (1 + 0.25) = \text{R} 7.288 \times 1.25 = \text{R} 9.11 \][/tex]
So, the selling price should be R9.11 per cup.
---
### 3.4 Determine Mary's fixed costs per day.
Mary's fixed costs per day include the stall cost and the travel cost:
[tex]\[ \text{Fixed Costs} = \text{R} 40 + \text{R} 14.20 = \text{R} 54.20 \][/tex]
---
### 3.5 Provide an equation for the expenses of selling coffee per day.
Let the number of cups of coffee sold per day be denoted as [tex]\( x \)[/tex].
The total expense per day [tex]\( E(x) \)[/tex] includes the fixed costs and the variable cost per cup of coffee. The variable cost per cup is [tex]\( C = \text{R} 7.288 \)[/tex]:
[tex]\[ E(x) = \text{Fixed Costs} + \text{(Cost per cup)} \times \text{(Number of cups sold)} \][/tex]
[tex]\[ E(x) = \text{R} 54.20 + \text{R} 7.288 \times x \][/tex]
---
### 3.6 Mary decides to sell the coffee at R10,00 per cup.
At this point, since the graph is not provided, we cannot directly reference it. However, generally, from the income and expenses graphs, you would be able to determine the break-even point, profit, and loss based on the number of cups sold.
Knowing that the selling price is R10.00 per cup, you can set up the income equation:
[tex]\[ \text{Income}(x) = \text{Selling Price} \times x \][/tex]
[tex]\[ \text{Income}(x) = \text{R} 10.00 \times x \][/tex]
You can then compare the income and expense equations to determine profitability and other financial metrics.
