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This is $20,000 × 8 × .70. This is not the correct way to calculate the total manufacturing cost for eight propellers.
This answer results from multiplying $20,000 by .7 and getting $14,000; then multiplying $14,000 by .7 and getting $9,800; then multiplying $9,800 by .7 and getting $6,860; then summing $20,000 + $14,000 + $9,800 + $6,860 = $50,660. Under the Incremental Unit-Time Learning Model, $20,000 is the cost of the first unit; $14,000 is the cost of the second unit; $9,800 is the cost of the fourth unit; and $6,860 is the cost of the eighth unit. This is incorrect for two reasons: (1) the problem says to use the Cumulative Average-Time Learning Model, not the Incremental Unit-Time Learning Model; and (2) this would not be correct even for the Incremental Unit-Time Learning Model, because only the costs of the first, second, fourth and eighth units are included in the total.
The total cost to produce eight propellers, using the Cumulative Average-Time Learning Model, is $20,000 (2 × .70) (2 × .70) (2 × .70), or $20,000 (2 × .70)3 = $54,880. Another way to calculate the total cost under the Cumulative Average-Time Learning Model is to find the average cost per unit and multiply it by the number of units produced. To find the average cost per unit using the Cumulative Average-Time Learning Model, multiply the cost for the first unit by the learning curve rate raised to the appropriate exponent for the number of times doubling will occur. For eight units, doubling will occur three times (from 1 unit to 2 units; from 2 units to 4 units; and from 4 units to 8 units). $20,000 × .73 = $6,860. The total cost is the average cost of $6,860 × 8, which equals $54,880.
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