Mighty Muffler Inc., operates an automobile service facility. The table below shows that cost incurred during a month when 600 mufflers were replaced. Number of Mufflers Replaced Total costs : 500 600 700 Fixed costs A $8,400 C Variable costs B 24,000 D Total costs E $32,400 F === ====== === Cost per muffler replacement : Fixed cost G H I Variable cost J K L Total cost per muffler replacement M N O == == == Required : Fill in the missing amounts, labeled A through O, in the table.
The Correct Answer and Explanation is :
Explanation:
The table shows the cost structure for Mighty Muffler Inc., based on the number of mufflers replaced in a month. Here’s how the missing values were determined:
- Fixed Costs (A, C)
Fixed costs remain constant regardless of the number of mufflers replaced. Given that fixed costs for 600 mufflers are $8,400, they remain the same for 500 and 700 replacements. - Variable Costs (B, D)
Variable costs are proportional to the number of mufflers replaced.
- The variable cost per muffler is $24,000 ÷ 600 = $40.
- For 500 mufflers, variable cost = 500 × $40 = $20,000.
- For 700 mufflers, variable cost = 700 × $40 = $28,000.
- Total Costs (E, F)
Total cost = Fixed cost + Variable cost.
- For 500 mufflers: $8,400 + $20,000 = $28,400.
- For 600 mufflers (given): $32,400.
- For 700 mufflers: $8,400 + $28,000 = $36,400.
- Cost per Muffler Replacement
- Fixed Cost per Muffler
- 500 mufflers: $8,400 ÷ 500 = $16.80
- 600 mufflers: $8,400 ÷ 600 = $14.00
- 700 mufflers: $8,400 ÷ 700 = $12.00
- Variable Cost per Muffler remains constant at $40.
- Total Cost per Muffler
- 500 mufflers: $28,400 ÷ 500 = $56.80
- 600 mufflers: $32,400 ÷ 600 = $54.00
- 700 mufflers: $36,400 ÷ 700 = $52.00
This analysis shows that as more mufflers are replaced, the total cost increases, but the total cost per muffler decreases due to spreading the fixed costs over more units.