Perteet Corporation's relevant range of activity is 6,600 units to 13,000 units. When it produces and sells 9,800 units, its average costs per unit are as follows: If 6,400 units are produced, the total amount of manufacturing overhead cost is closest to:
A) $31,360
B) $54,060
C) $41,900
D) $24,320

Question

Perteet Corporation's relevant range of activity is 6,600 units to 13,000 units. When it produces and sells 9,800 units, its average costs per unit are as follows:  If 6,400 units are produced, the total amount of manufacturing overhead cost is closest to:
A) $31,360 
B) $54,060 
C) $41,900 
D) $24,320

Quizplus · Accepted Answer

To solve the problem, we need to use the high-low method to determine the variable cost per unit and the total fixed cost.

Step 1: Calculate the variable cost per unit:

Variable cost per unit = (Cost at highest activity level - Cost at lowest activity level) ÷ (Highest activity level - Lowest activity level)
Variable cost per unit = ($129,800 - $85,800) ÷ (13,000 - 6,600) = $8

Step 2: Use the total cost equation to calculate the total fixed cost:

Total cost = Total fixed cost + (Variable cost per unit × Number of units)

We know that when 9,800 units are produced, the average cost per unit is $10.52. Using this information, we can solve for the total fixed cost:

$10.52 × 9,800 = Total fixed cost + ($8 × 9,800)
$103,096 = Total fixed cost + $78,400
Total fixed cost = $24,696

Step 3: Use the total cost equation again to calculate the total manufacturing overhead cost when 6,400 units are produced:

Total cost = Total fixed cost + (Variable cost per unit × Number of units)

Total manufacturing overhead cost = Total fixed cost + (Variable cost per unit × Number of units) 
Total manufacturing overhead cost = $24,696 + ($8 × 6,400) 
Total manufacturing overhead cost = $41,896

Therefore, the closest answer is C) $41,900.

Perteet Corporation's Relevant Range of Activity Is 6,600 Units to 13,000