Answer :
Let's break down the problem step-by-step to address each part of the question and provide a detailed solution.
### 1. Calculate the Selling Price for Each Brand
Vuyo's markup on all sunglasses is 40%. The cost per pair and the selling prices are calculated as follows:
- Brand A:
- Cost per pair = 100
- Selling price = Cost per pair + 40% markup = 100 (1 + 0.40) = 140
- Brand B:
- Cost per pair = 150
- Selling price = Cost per pair + 40% markup = 150 (1 + 0.40) = 210
- Brand C:
- Cost per pair = 300
- Selling price = Cost per pair + 40% markup = 300 (1 + 0.40) = 420
Thus, the selling prices for each brand are:
- Brand A: 140
- Brand B: 210
- Brand C: 420
### 2. Profit if All Sunglasses Are Sold
To find the profit, we need to calculate the total cost and total revenue if all sunglasses are sold, and then find the difference.
- Total Cost:
- Brand A: 100 300 = 30,000
- Brand B: 150 200 = 30,000
- Brand C: 300 100 = 30,000
- Total Cost = 30,000 + 30,000 + 30,000 = 90,000
- Total Revenue:
- Brand A: 140 300 = 42,000
- Brand B: 210 200 = 42,000
- Brand C: 420 100 = 42,000
- Total Revenue = 42,000 + 42,000 + 42,000 = 126,000
- Total Profit:
- Total Profit = Total Revenue - Total Cost = 126,000 - 90,000 = 36,000
### 3. Total Income After Discounting Brand C Sunglasses
Vuyo has sold 4 pairs of Brand C sunglasses at the original price. Now he decides to discount the remaining Brand C sunglasses by 30%.
- Remaining Brand C pairs:
- Initial Quantity: 100
- Sold Pairs: 4
- Remaining pairs = 100 - 4 = 96
- Discounted Selling Price for Brand C:
- Original Selling Price: 420
- Discount Percentage: 30%
- Discounted Price = 420 (1 - 0.30) = 294
Now, we calculate the total income considering the sale of 4 pairs at the original price and 96 pairs at the discounted price.
- Income from Brand C:
- Income for 4 pairs: 4 420 = 1,680
- Income for remaining 96 pairs: 96 294 = 28,224
- Total Income for Brand C = 1,680 + 28,224 = 29,904
- Total Income:
- Total Income = Income from Brand A + Income from Brand B + Income from Brand C
- Income from Brand A: 42,000
- Income from Brand B: 42,000
- Total Income = 42,000 + 42,000 + 29,904 = 113,904
### 4. Profit on Brand C Sunglasses
To determine the profit specifically for Brand C sunglasses:
- Total Cost for Brand C:
- Cost per pair: 300
- Quantity bought: 100
- Total Cost = 300 100 = 30,000
- Total Revenue for Brand C:
- Revenue from 4 pairs at original price: 4 420 = 1,680
- Revenue from 96 pairs at discounted price: 96 * 294 = 28,224
- Total Revenue = 1,680 + 28,224 = 29,904
- Profit for Brand C:
- Profit = Total Revenue - Total Cost = 29,904 - 30,000 = -96
### 5. Conclusion
Given the negative profit for Brand C, Vuyo made a loss of 96 on Brand C sunglasses after discounting them.
### 6. Decision on Discounting
- Profit Analysis:
- Overall, Vuyo made a net profit of 36,000 if all sunglasses had been sold at the original prices.
- After the discount, his total income turned out to be 113,904, and the loss on Brand C was 96.
Considering these factors, the decision to discount the Brand C sunglasses after 8 months prevented them from being unsold entirely, which could have resulted in an even larger loss. Therefore, while the discount led to a small loss specifically on Brand C, it was likely a wise decision to generate some revenue and clear inventory.
### 1. Calculate the Selling Price for Each Brand
Vuyo's markup on all sunglasses is 40%. The cost per pair and the selling prices are calculated as follows:
- Brand A:
- Cost per pair = 100
- Selling price = Cost per pair + 40% markup = 100 (1 + 0.40) = 140
- Brand B:
- Cost per pair = 150
- Selling price = Cost per pair + 40% markup = 150 (1 + 0.40) = 210
- Brand C:
- Cost per pair = 300
- Selling price = Cost per pair + 40% markup = 300 (1 + 0.40) = 420
Thus, the selling prices for each brand are:
- Brand A: 140
- Brand B: 210
- Brand C: 420
### 2. Profit if All Sunglasses Are Sold
To find the profit, we need to calculate the total cost and total revenue if all sunglasses are sold, and then find the difference.
- Total Cost:
- Brand A: 100 300 = 30,000
- Brand B: 150 200 = 30,000
- Brand C: 300 100 = 30,000
- Total Cost = 30,000 + 30,000 + 30,000 = 90,000
- Total Revenue:
- Brand A: 140 300 = 42,000
- Brand B: 210 200 = 42,000
- Brand C: 420 100 = 42,000
- Total Revenue = 42,000 + 42,000 + 42,000 = 126,000
- Total Profit:
- Total Profit = Total Revenue - Total Cost = 126,000 - 90,000 = 36,000
### 3. Total Income After Discounting Brand C Sunglasses
Vuyo has sold 4 pairs of Brand C sunglasses at the original price. Now he decides to discount the remaining Brand C sunglasses by 30%.
- Remaining Brand C pairs:
- Initial Quantity: 100
- Sold Pairs: 4
- Remaining pairs = 100 - 4 = 96
- Discounted Selling Price for Brand C:
- Original Selling Price: 420
- Discount Percentage: 30%
- Discounted Price = 420 (1 - 0.30) = 294
Now, we calculate the total income considering the sale of 4 pairs at the original price and 96 pairs at the discounted price.
- Income from Brand C:
- Income for 4 pairs: 4 420 = 1,680
- Income for remaining 96 pairs: 96 294 = 28,224
- Total Income for Brand C = 1,680 + 28,224 = 29,904
- Total Income:
- Total Income = Income from Brand A + Income from Brand B + Income from Brand C
- Income from Brand A: 42,000
- Income from Brand B: 42,000
- Total Income = 42,000 + 42,000 + 29,904 = 113,904
### 4. Profit on Brand C Sunglasses
To determine the profit specifically for Brand C sunglasses:
- Total Cost for Brand C:
- Cost per pair: 300
- Quantity bought: 100
- Total Cost = 300 100 = 30,000
- Total Revenue for Brand C:
- Revenue from 4 pairs at original price: 4 420 = 1,680
- Revenue from 96 pairs at discounted price: 96 * 294 = 28,224
- Total Revenue = 1,680 + 28,224 = 29,904
- Profit for Brand C:
- Profit = Total Revenue - Total Cost = 29,904 - 30,000 = -96
### 5. Conclusion
Given the negative profit for Brand C, Vuyo made a loss of 96 on Brand C sunglasses after discounting them.
### 6. Decision on Discounting
- Profit Analysis:
- Overall, Vuyo made a net profit of 36,000 if all sunglasses had been sold at the original prices.
- After the discount, his total income turned out to be 113,904, and the loss on Brand C was 96.
Considering these factors, the decision to discount the Brand C sunglasses after 8 months prevented them from being unsold entirely, which could have resulted in an even larger loss. Therefore, while the discount led to a small loss specifically on Brand C, it was likely a wise decision to generate some revenue and clear inventory.
