Math Problem Statement

Riya Khatri, contract negotiator for Nebula Airframe Company, is currently involved in bidding on a follow-up government contract. In gathering cost data from the first three units, which Nebula produced under a research and development contract, she found that the first unit took 3,000 labor hours, the second took 2,700 labor hours, and the third took 2,540 hours. Use Exhibit 6.5.

In a contract for three more units, how many labor hours should Khatri plan for?

Note: Round your answer to the nearest whole number. this is exhibit 6.5 "Cumulative Improvement Factor Unit 60% 65% 70% 75% 80% 85% 90% 95% 1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 2 1.600 1.650 1.700 1.750 1.800 1.850 1.900 1.950 3 2.045 2.155 2.268 2.384 2.502 2.623 2.746 2.872 4 2.405 2.578 2.758 2.946 3.142 3.345 3.556 3.774 5 2.710 2.946 3.195 3.459 3.738 4.031 4.339 4.662 6 2.977 3.274 3.593 3.934 4.299 4.688 5.101 5.538 7 3.216 3.572 3.960 4.380 4.834 5.322 5.845 6.404 8 3.432 3.847 4.303 4.802 5.346 5.936 6.574 7.261 9 3.630 4.102 4.626 5.204 5.839 6.533 7.290 8.111 10 3.813 4.341 4.931 5.589 6.315 7.116 7.994 8.955 12 4.144 4.780 5.501 6.315 7.227 8.244 9.374 10.62 14 4.438 5.177 6.026 6.994 8.092 9.331 10.72 12.27 16 4.704 5.541 6.514 7.635 8.920 10.38 12.04 13.91 18 4.946 5.879 6.972 8.245 9.716 11.41 13.33 15.52 20 5.171 6.195 7.407 8.828 10.48 12.40 14.61 17.13 22 5.379 6.492 7.819 9.388 11.23 13.38 15.86 18.72 24 5.574 6.773 8.213 9.928 11.95 14.33 17.10 20.31 25 5.668 6.909 8.404 10.19 12.31 14.80 17.71 21.10 30 6.097 7.540 9.305 11.45 14.02 17.09 20.73 25.00 35 6.478 8.109 10.13 12.72 15.64 19.29 23.67 28.86 40 6.821 8.631 10.90 13.72 17.19 21.43 26.54 32.68 45 7.134 9.114 11.62 14.77 18.68 23.50 29.37 36.47 50 7.422 9.565 12.31 15.78 20.12 25.51 32.14 40.22 60 7.941 10.39 13.57 17.67 22.87 29.41 37.57 47.65 70 8.401 11.13 14.74 19.43 25.47 33.17 42.87 54.99 80 8.814 11.82 15.82 21.09 27.96 36.80 48.05 62.25 90 9.191 12.45 16.83 22.67 30.35 40.32 53.14 69.45 100 9.539 13.03 17.79 24.18 32.65 43.75 58.14 76.59 120 10.16 14.11 19.57 27.02 37.05 50.39 67.93 90.71 140 10.72 15.08 21.20 29.67 41.22 56.78 77.46 104.7 160 11.21 15.97 22.72 32.17 45.20 62.95 86.80 118.5 180 11.67 16.79 24.14 34.54 49.03 68.95 95.96 132.1 200 12.09 17.55 25.48 36.80 52.72 74.79 105.0 145.7 250 13.01 19.28 28.56 42.05 61.47 88.83 126.9 179.2 300 13.81 20.81 31.34 46.94 69.66 102.2 148.2 212.2 350 14.51 22.18 33.89 51.48 77.43 115.1 169.0 244.8 400 15.14 23.44 36.26 55.75 84.85 127.6 189.3 277.0 450 15.72 24.60 38.48 59.80 91.97 139.7 209.2 309.0 500 16.26 25.68 40.58 63.68 98.85 151.5 228.8 340.6 600 17.21 27.67 44.47 70.97 112.0 174.2 267.1 403.3 700 18.06 29.45 48.04 77.77 124.4 196.1 304.5 465.3 800 18.82 31.09 51.36 84.18 136.3 217.3 341.0 526.5 900 19.51 32.60 54.46 90.26 147.7 237.9 376.9 587.2 1,000 20.15 31.01 57.40 96.07 158.7 257.9 412.2 647.4 1,200 21.30 36.59 62.85 107.0 179.7 296.6 481.2 766.6 1,400 22.32 38.92 67.85 117.2 199.6 333.9 548.4 884.2 1,600 23.23 41.04 72.49 126.8 218.6 369.9 614.2 1001 1,800 24.06 43.00 76.85 135.9 236.8 404.9 678.8 1116 2,000 24.83 44.84 80.96 144.7 254.4 438.9 742.3 1230 2,500 26.53 48.97 90.39 165.0 296.1 520.8 897.0 1513 3,000 27.99 52.62 98.90 183.7 335.2 598.9 1047 1791"

Solution

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Math Problem Analysis

Mathematical Concepts

Learning Curves
Cumulative Improvement Factors

Formulas

Learning rate formula: r = (Time for the second unit) / (Time for the first unit)

Theorems

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Suitable Grade Level

Graduate Level