Let's break down the problem into its parts and explain how to create the pie charts as well as the logic behind the profit-sharing structure.
A. Pie Chart of Investments
Each individual invested the following amounts:
- A: $30,000
- B: $40,000
- C: $60,000
- D: $70,000
Step 1: Calculate Total Investment To draw a pie chart for investments, we first calculate the total investment made by all parties.
\[ \text{Total Investment} = A + B + C + D = 30,000 + 40,000 + 60,000 + 70,000 = 200,000 \]
Step 2: Calculate Each Person's Percentage of the Total Investment Next, we determine what percentage of the total each person's investment constitutes.
- A: \(\frac{30,000}{200,000} \times 100 = 15%\)
- B: \(\frac{40,000}{200,000} \times 100 = 20%\)
- C: \(\frac{60,000}{200,000} \times 100 = 30%\)
- D: \(\frac{70,000}{200,000} \times 100 = 35%\)
Step 3: Create the Pie Chart To create a pie chart:
- Each slice will represent the percentage of each person's investment from the total.
- A will have a slice of 15%, B will have 20%, C will have 30%, and D will have 35%.
B. Pie Chart Showing Profit Division
Step 1: Determine the Profit Distribution Let’s assume the total profit from the business is \(P\). A, as the manager, will receive one-third of the profits, and the remaining two-thirds will be distributed based on investment proportions.
Profit Distribution Breakdown:
- A's share as manager: \(\frac{1}{3}P\)
- Remaining profit to distribute: \( \frac{2}{3}P \)
Step 2: Calculate Each Person's Share of the Remaining Profit The remaining profit will be distributed based on their investments.
Step 3: Create the Individual Shares for Equity Distribution
- Total investment portions (as calculated earlier) can be used:
- Total investment reference: \(200,000\)
- Proportion of remaining profit for each:
- B's share of excess share: \(\frac{40,000}{200,000} = 0.2\)
- C's share of excess share: \(\frac{60,000}{200,000} = 0.3\)
- D's share of excess share: \(\frac{70,000}{200,000} = 0.35\)
Using these proportions, each person’s total share of profit \(P\) can be calculated:
- A's total share: \(\frac{1}{3}P + \frac{2}{3}P \times \frac{30,000}{200,000}\)
- B's total share: \(\frac{2}{3}P \times 0.2\)
- C's total share: \(\frac{2}{3}P \times 0.3\)
- D's total share: \(\frac{2}{3}P \times 0.35\)
Let’s combine the distribution:
- A's total share: \(\frac{1}{3}P + \frac{1}{20}P = \frac{7}{15}P\)
- B's share: \(\frac{2}{3} \times \frac{1}{5}P = \frac{2}{15}P\)
- C's share: \(\frac{2}{3} \times \frac{3}{10}P = \frac{2}{10}P = \frac{4}{15}P\)
- D's share: \(\frac{2}{3} \times \frac{7}{20}P = \frac{7}{30}P \approx \frac{7}{15}P\)
Total to check:
- Total profit shared is distributed as:
- A: \(\frac{1}{3}P + \frac{0.15}{P} = \frac{1/3 + 0.15}{P} = A\)
- B: based on investment similar calculations
Step 4: Any profit \(P\), Calculate for actual percentages.
Summary of Pie Charts
-
First Pie Chart (Investments)
- A: 15%
- B: 20%
- C: 30%
- D: 35%
-
Second Pie Chart (Profit Division)
- Allocate \(P\) as per previously calculated ratios using the outlined shares after A's manager share is set aside.
Creating the actual graphics of the pie charts can be done using software like Excel, Google Sheets, or any online graph-making tool, where values can easily be input, and it'll render the necessary visual representation.
Conclusion
This thorough explanation provides a comprehensive methodology for calculating both the investment ratios for a pie chart and the profit-sharing strategy under a unique manager compensation scheme while explaining the thought process at each step.