Answer :
Alright, let's go through the problem step by step and calculate the necessary values.
To start, we'll fill in the missing values [tex]\(\text{A}\)[/tex], [tex]\(\text{B}\)[/tex], and [tex]\(\text{C}\)[/tex] based on the given data.
Here is the initial table information reconstructed in textual form for clarity:
1. Month 1: Cost = [tex]\(5 \rightarrow 200\)[/tex], Selling price = [tex]\(24 \times 5\)[/tex], Profit = 22900
2. Month 2: Cost = [tex]\(11700\)[/tex], Selling price = [tex]\(9600\)[/tex]
3. Month 3: Profit = 7500
4. Month 4: Selling price = [tex]\(21000\)[/tex]
Given that:
- Month 1:
- Cost Price: [tex]\(200 \text{ (Cost of each item) } \times 5 \text{ (Number of items)} = 1000\)[/tex]
- Selling Price: [tex]\(24 \times 5 = 120\)[/tex]
- Profit = 22900
- Month 2:
- Cost: 11700
- Selling Price: 9600
- Month 3:
- Profit: 7500
- Month 4:
- Selling Price: 21000
### Step-by-Step Solution
1. Determine [tex]\(\text{A}\)[/tex]:
To find the selling price of the first month ([tex]\(A\)[/tex]):
[tex]\[ \text{Profit (Month 1)} = \text{Selling Price (Month 1)} - \text{Cost Price (Month 1)} \][/tex]
[tex]\[ 22900 = A - 1000 \][/tex]
[tex]\[ A = 22900 + 1000 = 23900 \][/tex]
Thus, [tex]\(A = 23900\)[/tex].
2. Determine the selling price for Month 3:
Since we know the cost in Month 2 and the profit in Month 3, we can find the selling price of Month 3. However, we must find the cost of Month 3 first. Let the cost be [tex]\( \text{Cost}_{\text{Month3}} \)[/tex].
[tex]\[ \text{Profit (Month 3)} = \text{Selling Price (Month 3)} - \text{Cost}_{\text{Month3}} \][/tex]
If we assume the cost structure for Month 3 follows a simple trend of arithmetic mean:
[tex]\[ \text{Cost}_{\text{Month3}} = \frac{\text{Cost (Month 2)} + \text{Cost (Month 4)}}{2} = \frac{11700 + 14200}{2} = 12950 \][/tex]
Selling Price in Month 3:
[tex]\[ B = \text{Profit (Month 3)} + \text{Cost}_{\text{Month3}} = 7500 + 12950 = 20450 \][/tex]
Thus, [tex]\(B = 20450\)[/tex].
3. Determine [tex]\(\text{Cost}_{\text{Month4}}\)[/tex] based on profit trend:
Since [tex]\(C\)[/tex] should reflect the profit from month 3, we'll use the trend to assume the cost.
[tex]\( \text{Cost}_{\text{Month4}} = \frac{23900 - 14400} = 9500 ) Thus, \(C = 13500\)[/tex].
Thus our values are:
- [tex]\(\text{A} = 23900\)[/tex]
- [tex]\(\text{B} = 20450\)[/tex]
- [tex]\(\text{C} = 13500\)[/tex]
### Step 4: Determine if Profit is Increasing, Decreasing, or Discrete
To determine the profit trend, consider the given profit values:
- Profit in Month 1: 22900
- Profit in Month 3: 7500
Comparing Month 1 and Month 3 shows a decrease.
Thus, the profit trend is decreasing.
### Step 5: Comment on Business Demand Fluctuation
Considering the seasonal impact on coats and jackets demand, it is safe to assume:
- Demand might peak during colder months (winter or rainy seasons).
- Demand might drop during warmer months.
Thus, it's unlikely that the business will have consistent demand throughout the year. Seasonal fluctuations are expected.
### Step 6: Draw a Line Graph
To draw a line graph of the given information:
- Plot the number of items over the months on the x-axis.
- Show cost and profits on the y-axis.
The graph will indicate the trend visually and must be clearly labeled with legends for 'Cost', 'Profit', and 'Number of Items'.
Ensure the graph is well-constructed with labeled axes, title, and a legend for clarity.
Here is an example pseudocode for drawing the graph in your head:
```
months = ["1st month", "2nd month", "3rd month", "4th month", "5th month"]
cost = [1000, 11700, 12950, 13500, None] # Estimated or given costs
profits = [22900, None, 7500, None, None] # Given profits
items = [5, 10, 15, 20, 25]
# Plotting logic will go here (use available graph plotting library to get the result you visualized)
# Ensure you have your months on the x-axis and costs, profits on the y-axis after converting them numerically.
```
In conclusion:
- [tex]\(\text{A} = 23900\)[/tex]
- [tex]\(\text{B} = 20450\)[/tex]
- [tex]\(\text{C} = 13500\)[/tex]
- Profit trend: Decreasing
- Business demand is likely seasonal and not consistent year-round.
To start, we'll fill in the missing values [tex]\(\text{A}\)[/tex], [tex]\(\text{B}\)[/tex], and [tex]\(\text{C}\)[/tex] based on the given data.
Here is the initial table information reconstructed in textual form for clarity:
1. Month 1: Cost = [tex]\(5 \rightarrow 200\)[/tex], Selling price = [tex]\(24 \times 5\)[/tex], Profit = 22900
2. Month 2: Cost = [tex]\(11700\)[/tex], Selling price = [tex]\(9600\)[/tex]
3. Month 3: Profit = 7500
4. Month 4: Selling price = [tex]\(21000\)[/tex]
Given that:
- Month 1:
- Cost Price: [tex]\(200 \text{ (Cost of each item) } \times 5 \text{ (Number of items)} = 1000\)[/tex]
- Selling Price: [tex]\(24 \times 5 = 120\)[/tex]
- Profit = 22900
- Month 2:
- Cost: 11700
- Selling Price: 9600
- Month 3:
- Profit: 7500
- Month 4:
- Selling Price: 21000
### Step-by-Step Solution
1. Determine [tex]\(\text{A}\)[/tex]:
To find the selling price of the first month ([tex]\(A\)[/tex]):
[tex]\[ \text{Profit (Month 1)} = \text{Selling Price (Month 1)} - \text{Cost Price (Month 1)} \][/tex]
[tex]\[ 22900 = A - 1000 \][/tex]
[tex]\[ A = 22900 + 1000 = 23900 \][/tex]
Thus, [tex]\(A = 23900\)[/tex].
2. Determine the selling price for Month 3:
Since we know the cost in Month 2 and the profit in Month 3, we can find the selling price of Month 3. However, we must find the cost of Month 3 first. Let the cost be [tex]\( \text{Cost}_{\text{Month3}} \)[/tex].
[tex]\[ \text{Profit (Month 3)} = \text{Selling Price (Month 3)} - \text{Cost}_{\text{Month3}} \][/tex]
If we assume the cost structure for Month 3 follows a simple trend of arithmetic mean:
[tex]\[ \text{Cost}_{\text{Month3}} = \frac{\text{Cost (Month 2)} + \text{Cost (Month 4)}}{2} = \frac{11700 + 14200}{2} = 12950 \][/tex]
Selling Price in Month 3:
[tex]\[ B = \text{Profit (Month 3)} + \text{Cost}_{\text{Month3}} = 7500 + 12950 = 20450 \][/tex]
Thus, [tex]\(B = 20450\)[/tex].
3. Determine [tex]\(\text{Cost}_{\text{Month4}}\)[/tex] based on profit trend:
Since [tex]\(C\)[/tex] should reflect the profit from month 3, we'll use the trend to assume the cost.
[tex]\( \text{Cost}_{\text{Month4}} = \frac{23900 - 14400} = 9500 ) Thus, \(C = 13500\)[/tex].
Thus our values are:
- [tex]\(\text{A} = 23900\)[/tex]
- [tex]\(\text{B} = 20450\)[/tex]
- [tex]\(\text{C} = 13500\)[/tex]
### Step 4: Determine if Profit is Increasing, Decreasing, or Discrete
To determine the profit trend, consider the given profit values:
- Profit in Month 1: 22900
- Profit in Month 3: 7500
Comparing Month 1 and Month 3 shows a decrease.
Thus, the profit trend is decreasing.
### Step 5: Comment on Business Demand Fluctuation
Considering the seasonal impact on coats and jackets demand, it is safe to assume:
- Demand might peak during colder months (winter or rainy seasons).
- Demand might drop during warmer months.
Thus, it's unlikely that the business will have consistent demand throughout the year. Seasonal fluctuations are expected.
### Step 6: Draw a Line Graph
To draw a line graph of the given information:
- Plot the number of items over the months on the x-axis.
- Show cost and profits on the y-axis.
The graph will indicate the trend visually and must be clearly labeled with legends for 'Cost', 'Profit', and 'Number of Items'.
Ensure the graph is well-constructed with labeled axes, title, and a legend for clarity.
Here is an example pseudocode for drawing the graph in your head:
```
months = ["1st month", "2nd month", "3rd month", "4th month", "5th month"]
cost = [1000, 11700, 12950, 13500, None] # Estimated or given costs
profits = [22900, None, 7500, None, None] # Given profits
items = [5, 10, 15, 20, 25]
# Plotting logic will go here (use available graph plotting library to get the result you visualized)
# Ensure you have your months on the x-axis and costs, profits on the y-axis after converting them numerically.
```
In conclusion:
- [tex]\(\text{A} = 23900\)[/tex]
- [tex]\(\text{B} = 20450\)[/tex]
- [tex]\(\text{C} = 13500\)[/tex]
- Profit trend: Decreasing
- Business demand is likely seasonal and not consistent year-round.
