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Direct manufacturing laborhours required to make

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Unformatted text preview: 7 8 Cumulative Average Time per Unit (y): Labor Hours (2) 3,000 2,700 = (3,000 ´ 0.90) 2,539 2,430 = (2,700 ´ 0.90) 2,349 2,285 2,232 2,187 = (2,430 ´ 0.90) Cumulative Total Time: Labor­Hours (3) = (1) ´ (2) 3,000 5,400 7,616 9,720 11,745 13,710 15,624 17,496 Alternat ively, to compute the values in co lumn (2) we could use the formula y = aXb where a = 3,000, X = 2, 4, or 8, and b = – 0.152004, which gives – when X = 2, y = 3,000 ´ 2 0.152004 = 2,700 – when X = 4, y = 3,000 ´ 4 0.152004 = 2,430 – when X = 8, y = 3,000 ´ 8 0.152004 = 2,187 Variable Costs of Producing 2 Units 4 Units 8 Units \$160,000 \$320,000 \$ 640,000 135,000 81,000 \$376,000 243,000 145,800 \$708,800 437,400 262,440 \$1,339,840 Direct materials \$80,000 ´ 2; 4; 8 Direct manufacturing labor \$25 ´ 5,400; 9,720; 17,496 Variable manufacturing overhead \$15 ´ 5,400; 9,720; 17,496 Total variable costs 10­17 10­30 (20 min.) Learning curve, incremental unit­time learning model. 1. The direct manufacturing labor­hours (DMLH) required to produce the first 2, 3, and 4 units, given the assumpt ion of an incremental unit­time learning curve of 90%, is as fo llows: 90% Learning Curve Cumulative Individual Unit Time for Xth Cumulative Total Time: Number of Units (X) Unit (y): Labor Hours Labor­Hours (1) (2) (3) 1 3,000 3,000 2 2,700 = (3,000 ´ 0.90) 5,700 3 2,539 8,239 4 2,430 = (2,700 ´ 0.90) 10,669 Values in co lumn (2) are calculated using the formula y = aXb where a = 3,000, X = 2, 3, or 4, and b = – 0.152004, which gives – when X = 2, y = 3,000 ´ 2 0.152004 = 2,700 – when X = 3, y = 3,000 ´ 3 0.152004 = 2,539 – when X = 4, y = 3,000 ´ 4 0.152004 = 2,430 Variable Costs of Producing 2 Units 3 Units 4 Units \$160,000 \$240,000 \$ 320,000 142,500 85,500 \$388,000 205,975 123,585 \$569,560 266,725 160,035 \$746,760 Direct materials \$80,000 ´ 2; 3; 4 Direct manufacturing labor \$25 ´ 5,700; 8,239; 10,669 Variable manufacturing overhead \$15 ´ 5,700; 8,239; 10,669 Total variable costs 2. Incremental unit­time learning model (fro m requirement 1) Cumulat ive average­t ime learning model (fro m Exercise 10­28) Difference Variable Costs of Pr...
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