Final answer:
The total production engineering cost per unit at an activity level of 8,900 machine-hours is $102.30.
Step-by-step explanation:
To calculate the total production engineering cost per unit at the new activity level, we need to consider that while variable costs change with the level of production, fixed costs remain constant within the relevant range.
Firstly, let's determine the variable cost per machine-hour by dividing the total variable production engineering cost by the number of machine-hours for the initial activity level. We have:
Total variable production engineering cost: $708,900
Initial machine-hours: 8,500
Variable cost per machine-hour = $708,900 / 8,500 = $83.40
Now with the variable cost per machine-hour figured out, we can find the total variable cost for the new activity level of 8,900 machine-hours by multiplying:
Variable cost per machine-hour x New machine-hours = $83.40 x 8,900 = $742,260
The total fixed production engineering cost doesn't change with the machine-hours, so it remains at:
Total fixed production engineering cost = $168,210
To find the total production engineering cost, we simply add the new variable cost to the fixed cost:
Total production engineering cost = Total fixed cost + New total variable cost
= $168,210 + $742,260
= $910,470
Finally, to determine the total production engineering cost per machine-hour for the 8,900 machine-hours level, divide the total production engineering cost by the number of machine-hours:
Total production engineering cost per machine-hour = $910,470 / 8,900 = $102.30