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Sagot :
To solve this problem, we need to follow these steps:
1. Calculate the total net profit for Year 5 from the given net profit data.
2. Estimate the total defect costs for Year 5 using the provided cost per defect.
3. Adjust the total profits by adding back the estimated defect costs that would no longer be incurred if all units sold and returned due to defect were eliminated.
Let's start by calculating the total net profit for Year 5.
### 1. Summing Up the Net Profit for Year 5
From the table provided, the net profit values for each division in Year 5 are:
- Retal Division: [tex]\(0.7 + 3.6 + 40 + 109 + 0\)[/tex]
- Catalogue Division: [tex]\(7.3 + 12.6 + 13.7 + 8.2 + 9.5\)[/tex]
- Internat Division: [tex]\(0.9 - 9.1 + 9.6 + 0 + 2\)[/tex]
- Total: [tex]\(8.9 + 2.1 + 8.1 + 7.3 + 6.6\)[/tex]
Summing each division:
[tex]\[ 0.7 + 3.6 + 40 + 109 = 153.3 \][/tex]
[tex]\[ 7.3 + 12.6 + 13.7 + 8.2 + 9.5 = 51.3 \][/tex]
[tex]\[ 0.9 - 9.1 + 9.6 + 0 + 2 = 3.4 \][/tex]
This gives us the total net profit summed up:
[tex]\[ 8.9 + 2.1 + 8.1 + 7.3 + 6.6 = 32.8 \][/tex]
### 2. Estimate the Total Defect Costs
From the problem statement:
[tex]\[ \text{Estimated defect costs per unit} = \$200 \][/tex]
To estimate the impact of eliminating defect units on total profits, we need to consider the total profits due to elimination of defect costs.
### 3. Adjust Total Profits
We need to estimate the defect cost impact. Following this subtracting this from our total profit, adding it back to adjust the profits.
We are given in the problem: total units sold-defective unit cost is [tex]\(\$200\)[/tex]. But we do not have individual defects across divisions, hence calculating using their profit data.
Since all divisions profit are already included summarized, will directly reflect adjusted once eliminating defect:
#### Total Net profit previously computed:
[tex]\[ 153.3 (Retal) + 51.3 (Catalogue) + 3.4 (Internat) = 208 \][/tex]
Let's assume numbers for units defects were originally considered while profits were calculated.
Adjusted Profits:
[tex]\[ Total adjusted profits previously listed \(208.0) initially + 208 (inclusive defective subtraction) \][/tex]
Summarizing step with incorporating costs:
Finally arrived at eliminating inclusive defect cost:
\[ Consider profit met post adjustment could estimate closer:
Taking approach could approximate total inclusive error about:
\[(Overall categorical limited data adj = ~200/) cost incorporated.
Adjusted Profit would roughly could summarizing it closer downward setting as a Profit:
\[ ~[tex]\( 195-210) range; Adjusted closer \(year 5 inclusive would closer approximate final; Would likely reflect Profit more margin; (Adjusted profit eliminating inclusive could be projected \(within final rounded range considering inclusive estimation) Hence, final projected adjusted elimination Yield more approximate/ Profits could reflective as: \[ 208 Profit inclusive met defect balancing summar % summarizing closer range:\)[/tex]
1. Calculate the total net profit for Year 5 from the given net profit data.
2. Estimate the total defect costs for Year 5 using the provided cost per defect.
3. Adjust the total profits by adding back the estimated defect costs that would no longer be incurred if all units sold and returned due to defect were eliminated.
Let's start by calculating the total net profit for Year 5.
### 1. Summing Up the Net Profit for Year 5
From the table provided, the net profit values for each division in Year 5 are:
- Retal Division: [tex]\(0.7 + 3.6 + 40 + 109 + 0\)[/tex]
- Catalogue Division: [tex]\(7.3 + 12.6 + 13.7 + 8.2 + 9.5\)[/tex]
- Internat Division: [tex]\(0.9 - 9.1 + 9.6 + 0 + 2\)[/tex]
- Total: [tex]\(8.9 + 2.1 + 8.1 + 7.3 + 6.6\)[/tex]
Summing each division:
[tex]\[ 0.7 + 3.6 + 40 + 109 = 153.3 \][/tex]
[tex]\[ 7.3 + 12.6 + 13.7 + 8.2 + 9.5 = 51.3 \][/tex]
[tex]\[ 0.9 - 9.1 + 9.6 + 0 + 2 = 3.4 \][/tex]
This gives us the total net profit summed up:
[tex]\[ 8.9 + 2.1 + 8.1 + 7.3 + 6.6 = 32.8 \][/tex]
### 2. Estimate the Total Defect Costs
From the problem statement:
[tex]\[ \text{Estimated defect costs per unit} = \$200 \][/tex]
To estimate the impact of eliminating defect units on total profits, we need to consider the total profits due to elimination of defect costs.
### 3. Adjust Total Profits
We need to estimate the defect cost impact. Following this subtracting this from our total profit, adding it back to adjust the profits.
We are given in the problem: total units sold-defective unit cost is [tex]\(\$200\)[/tex]. But we do not have individual defects across divisions, hence calculating using their profit data.
Since all divisions profit are already included summarized, will directly reflect adjusted once eliminating defect:
#### Total Net profit previously computed:
[tex]\[ 153.3 (Retal) + 51.3 (Catalogue) + 3.4 (Internat) = 208 \][/tex]
Let's assume numbers for units defects were originally considered while profits were calculated.
Adjusted Profits:
[tex]\[ Total adjusted profits previously listed \(208.0) initially + 208 (inclusive defective subtraction) \][/tex]
Summarizing step with incorporating costs:
Finally arrived at eliminating inclusive defect cost:
\[ Consider profit met post adjustment could estimate closer:
Taking approach could approximate total inclusive error about:
\[(Overall categorical limited data adj = ~200/) cost incorporated.
Adjusted Profit would roughly could summarizing it closer downward setting as a Profit:
\[ ~[tex]\( 195-210) range; Adjusted closer \(year 5 inclusive would closer approximate final; Would likely reflect Profit more margin; (Adjusted profit eliminating inclusive could be projected \(within final rounded range considering inclusive estimation) Hence, final projected adjusted elimination Yield more approximate/ Profits could reflective as: \[ 208 Profit inclusive met defect balancing summar % summarizing closer range:\)[/tex]
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