The table shows the cost structure of a firm producing computer mainframes. Calculate the missing values A through H and enter these into the boxes provided.
| Labor (hours) | Quantity | Fixed Cost ($) | Variable Cost ($) | Total Cost ($) | Marginal Cost ($) | Average Cost ($) | AVC* ($) |
|---------------|----------|-----------------|--------------------|----------------|-------------------|------------------|-----------|
| 0 | 0 | 10,000 | 0 | 10,000 | - | - | - |
| 40 | 18 | 10,000 | 5,000 | 15,000 | C | F | 277.78 |
| 50 | 45 | 10,000 | 10,000 | B | 185.19 | 444.44 | 222.22 |
| 60 | 65 | 10,000 | 15,000 | 25,000 | 250.00 | 384.62 | 230.77 |
| 70 | 78 | 10,000 | A | 30,000 | D | G | 256.41 |
| 80 | 88 | 10,000 | 25,000 | 35,000 | 500.00 | 397.73 | 284.09 |
| 90 | 94 | 10,000 | 30,000 | 40,000 | E | 425.53 | H |
*Average Variable Cost
Answer (1)
Calculate A (Variable Cost): A = 30000 − 10000 = 20000 .
Calculate B (Total Cost): B = 10000 + 10000 = 20000 .
Calculate C (Marginal Cost): C = ( 15000 − 10000 ) / ( 18 − 0 ) = 277.78 .
Calculate D (Marginal Cost): D = ( 30000 − 25000 ) / ( 78 − 65 ) = 384.62 .
Calculate E (Marginal Cost): E = ( 40000 − 35000 ) / ( 94 − 88 ) = 833.33 .
Calculate F (Average Cost): F = 15000/18 = 833.33 .
Calculate G (Average Cost): G = 30000/78 = 384.62 .
Calculate H (Average Variable Cost): H = 30000/94 = 319.15 .
The missing values are: A = 20000 , B = 20000 , C = 277.78 , D = 384.62 , E = 833.33 , F = 833.33 , G = 384.62 , H = 319.15 .
Explanation
Understanding the Problem We are given a table representing the cost structure of a firm producing computer mainframes. Our objective is to calculate the missing values A through H in the table. We will use the provided data and standard cost accounting formulas to determine these values.
Calculating A A represents the Variable Cost when Quantity = 78. We know that Total Cost = Fixed Cost + Variable Cost. From the table, when Quantity = 78, Total Cost = $30,000 and Fixed Cost = $10,000. Therefore, Variable Cost (A) = Total Cost - Fixed Cost.
Calculating A (Value) A = 30000 − 10000 = 20000
Calculating B B represents the Total Cost when Quantity = 45. We know that Total Cost = Fixed Cost + Variable Cost. From the table, when Quantity = 45, Fixed Cost = $10,000 and Variable Cost = $10,000. Therefore, Total Cost (B) = Fixed Cost + Variable Cost.
Calculating B (Value) B = 10000 + 10000 = 20000
Calculating C C represents the Marginal Cost when Labor = 40 hours. Marginal Cost = (Change in Total Cost) / (Change in Quantity). When Labor increases from 0 to 40 hours, Quantity increases from 0 to 18, and Total Cost increases from $10,000 to $15,000. Therefore, Marginal Cost (C) = (Change in Total Cost) / (Change in Quantity).
Calculating C (Value) C = ( 15000 − 10000 ) / ( 18 − 0 ) = 5000/18 = 277.78
Calculating D D represents the Marginal Cost when Quantity = 78. Marginal Cost = (Change in Total Cost) / (Change in Quantity). When Quantity increases from 65 to 78, Total Cost increases from $25,000 to $30,000. Therefore, Marginal Cost (D) = (Change in Total Cost) / (Change in Quantity).
Calculating D (Value) D = ( 30000 − 25000 ) / ( 78 − 65 ) = 5000/13 = 384.62
Calculating E E represents the Marginal Cost when Labor = 90 hours. Marginal Cost = (Change in Total Cost) / (Change in Quantity). When Quantity increases from 88 to 94, Total Cost increases from $35,000 to $40,000. Therefore, Marginal Cost (E) = (Change in Total Cost) / (Change in Quantity).
Calculating E (Value) E = ( 40000 − 35000 ) / ( 94 − 88 ) = 5000/6 = 833.33
Calculating F F represents the Average Cost when Labor = 40 hours. Average Cost = Total Cost / Quantity. When Labor = 40 hours, Quantity = 18 and Total Cost = $15,000. Therefore, Average Cost (F) = Total Cost / Quantity.
Calculating F (Value) F = 15000/18 = 833.33
Calculating G G represents the Average Cost when Quantity = 78. Average Cost = Total Cost / Quantity. When Quantity = 78, Total Cost = $30,000. Therefore, Average Cost (G) = Total Cost / Quantity.
Calculating G (Value) G = 30000/78 = 384.62
Calculating H H represents the Average Variable Cost when Labor = 90 hours. Average Variable Cost = Variable Cost / Quantity. When Labor = 90 hours, Quantity = 94 and Variable Cost = $30,000. Therefore, Average Variable Cost (H) = Variable Cost / Quantity.
Calculating H (Value) H = 30000/94 = 319.15
Final Answer The missing values are: A = $20,000, B = $20,000, C = $277.78, D = $384.62, E = $833.33, F = $833.33, G = $384.62, and H = $319.15.
Examples
Understanding cost structures is crucial in business for making informed decisions about pricing, production levels, and profitability. For instance, knowing the marginal cost helps a company determine the profitability of producing one more unit. Average cost is essential for setting prices that ensure the company covers its costs. By analyzing these cost components, businesses can optimize their operations and maximize profits. This type of analysis is used daily by businesses of all sizes to manage their finances effectively.
