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costacctg13_sm_ch10

# Solutionexhibit1038b plots and regressio n lines for

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Unformatted text preview: 87,160 370,185 \$3,538,085 1 he direct lab or hours to produce t he s econd thr ough t he eight h b oats can b e calcu lated via a table T for mat, given the assumption of an incr emental unit­time learning curve of 85%: 85% Learning Curve Cumulative Number of Units (X) (1) 1 2 3 4 5 6 7 8 Individual Unit Time for Xth Unit (y* ): Labor Hours (2) 10,000 8,500 = (10,000 ´ 0.85) 7,729 7,225 = (8,500 ´ 0.85) 6,857 6,570 6,337 6,141 = (7,225 ´ 0.85) Cumulative Total Time: Labor­Hours (3) 10,000 18,500 26,229 33,454 40,311 46,881 53,217 59,358 *Calculated as y = pXq where p = 10,000, q = – 0.234465, and X = 1, 2, 3,. . .8. The direct manufacturing labor­hours to produce the second through the eighth boat is 59,358 – 10,000 = 49,358 hours. 10­29 2. Difference in total costs to manufacture the second through the eighth boat under the incremental unit­time learning model and the cumulat ive average­time learning model is \$3,538,085 (calculated in requirement 1 of this problem) – \$2,949,975 (from requirement 1 of Problem 10­36) = \$588,110, i.e., the total costs are higher for the incremental unit­time model. The incremental unit­time learning curve has a slo wer rate of decline in the time required to produce successive units than does the cumulative average­time learning curve (see Proble m 10­35, requirement 1). Assuming the same 85% factor is used for both curves: Estimated Cumulative Direct Manufacturing Labor­Hours Cumulative Average­ Incremental Unit­Time Time Learning Model Learning Model 10,000 10,000 17,000 18,500 28,900 33,454 49,130 59,358 Cumulative Number of Units 1 2 4 8 The reason is that, in the incremental unit­time learning model, as the number o f unit s double, only the last unit produced has a cost of 85% of the init ial cost. In the cumulat ive average­t ime learning model, doubling the number of units causes the average cost of all the addit ional unit s produced (not just the last unit) to be 85% of the init ial cost. Nautilus should ex...
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