6-4

Lazer Technologies Inc. (LTI) has produced a total of 20 high-power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The 20 units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U.S. Department of Defense (DoD). Testing of the laser units has shown that they are effective defense weapons, and if redesigned to add portability and easier field maintenance, the units could be truck-mounted. The DoD has asked LTI to submit a bid for 100 more units. The 20 units that LTI has built so far cost the following amounts and are listed in the order in which they were produced: Use Exhibit 6.4 and Exhibit 6.5. UNIT NUMBER 1 2 3 4 COST ($ MILLIONS) $9.0 8.9 COST ($ MILLIONS) $13.0 11.4 11.0 10.3 10.2. 9.9 9.6 9.5 9.3 9.2 UNIT NUMBER 11 12 13 14 15 16 17 18 19 20 8.7 8.6 8.5 8.6 8.4 8.4 8.3 8.3 8 10 a. Based on past experience. what is the learning rate? (Do not round intermediate calculations. Round your answer to the a. Based on past experience, what is the learning rate? (Do not round intermediate calculations. Round your answer to the nearest whole percent.) Learning rate 90% b. What cost should LTI use in their bid for the total order of 100 additional units, assuming that learning continues? (Use your rounded learning rate from Part a. Enter your answer in millions of dollars rounded to one decimal place.) Cost for 120 more units million dollars c. What is the cost expected to be for the last unit under the learning rate you estimated? (Use your rounded learning rate from Part a. Enter your answer in millions of dollars rounded to one decimal place.) Expected cost for last unit million dollars Exhlblt 6.4 Improvement Curves: Table of Unit Values Unit Improvement Factor Unit 60% 65% 70% 75% 80% 85% 90% 95% 1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 2. .6000 .6500 .7000 .7500 .8000 .8500 9000 .9500 3 4450 .5052 .5682 6338 .7021 .7729 .8462 .9219 4 .3600 4225 4900 .5625 .6400 .7225 8100 .9025 5 3054 3678 4368 .5127 .5956 .6857 .7830 .8877 6 .2670 3284 3977 4754 .5617 .6570 .7616 .8758 7 .2383 .2984 .3674 4459 .5345 .6337 .7439 .8659 8 2160 2746 .3430 4219 .5120 .6141 .7290 .8574 9 .1980 2552 .3228 4017 .4930 .5974 .7 161 .8499 10 1832 .2391 .3058 3846 .4765 .5828 .7047 .8433 12 .1602 2135 2784 .3565 4493 .5584 .6854 .8320 14 .1430 .1940 2572 3344 .4276 .5386 .6696 .8226 16 .1290 .1785 .2401 3164 4096 .5220 .6561 .8145 18 .1188 .1659 .2260 .3013 .3944 .5078 .6445 .8074 20 .1099 .1554 .2141 2884 3812 .4954 .6342 .8012 22 .1025 .1465 2038 2772 3697 4844 .6251 .7955 24 0961 .1387 .1949 2674 .3595 4747 .6169 .7904 25 0933 .1353 .1908 2629 3548 4701 .6131 .7880 30 0815 .1208 .1737 2437 .3346 4505 .5963 .7775 35 0728 . 1097 .1605 2286 .3184 4345 -5825 .7687 40 .0660 .1010 1498 2163 .3050 .4211 .5708 .7611 45 .0605 .0939 .1410 2060 .2936 4096 .5607 .7545 50 .0560 0879 .1336 .1972 .2838 .3996 .5518 .7486 60 0489 .0785 .1216 1828 2676 .3829 5367 .7386 70 .0437 .07 13 1123 .17 15 .2547 .3693 .5243 .7302 80 0396 .0657 .1049 .1622 2440 3579 5137 .7231 90 0262 06.10 0987 1545 2349 3482 5046 7 168 Mexhibit_6.4.jpg 518x1,228 pixels 0 Hor 45 0605 .0939 1410 2060 .2936 4096 .5607 .7545 50 .0560 0879 .1336 .1972 .2838 .3996 .5518 .7486 60 .0489 .0785 1216 .1828 .2676 .3829 .5367 .7386 70 .0437 .0713 .1123 .17 15 .2547 .3693 .5243 .7302 80 0396 .0657 .1049 1622 .2440 .3579 5137 .7231 90 0363 .0610 .0987 1545 .2349 .3482 .5046 .7 168 100 0336 .0572 .0935 .1479 2271 .3397 .4966 .7112 120 .0294 .0510 .0851 .1371 .2141 .3255 4830 .7017 140 .0262 .0464 0786 .1287 .2038 .3139 4718 .6937 160 .0237 .0427 .0734 .1217 .1952 .3042 4623 .6869 180 0218 0397 .0691 .1159 .1879 .2959 4541 .6809 200 0201 0371 .0655 .1109 .1816 2887 4469 .6757 250 .0171 .0323 .0584 .1011 . 1691 .2740 4320 .6646 300 0149 .0289 .0531 .0937 . 1594 .2625 .4202 .6557 350 .0133 0262 .0491 .0879 .1517 .2532 4105 .6482 400 0121 0241 .0458 .0832 .1453 .2454 4022 .6419 450 .0111 .0224 .0431 0792 .1399 .2387 .3951 .6363 500 .0103 .0210 .0408 .0758 .1352 .2329 .3888 6314 600 0090 .0188 0372 0703 .1275 .2232 .3782 .6229 700 .0080 20171 0344 .0659 .1214 .2152 .3694 .6158 800 .0073 .0157 0321 .0624 .1163 .2086 .3620 .6098 900 .0067 0146 0302 .0594 1119 2029 .3556 .6045 1,000 .0062 .0137 0286 .0569 1082 .1980 .3499 .5998 1,200 0054 0122 0260 0527 .1020 .1897 .3404 .5918 1,400 .0048 0111 .0240 0495 .0971 .1830 .3325 5850 1,600 0044 .0102 .0225 .0468 .0930 .1773 3258 .5793 1.800 0040 .0095 0211 .0446 .0895 . 1725 3200 .5743 2,000 0037 .0089 0200 0427 .0866 1683 3149 .5698 2.500 0031 0077 0178 0389 0806 1597 3044 .5605 3,000 0027 .0069 0162 .0360 .0760 . 1530 .2961 5530 Exhibit 6.5 Amprovememe curves. Tavle urcumulauve values 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 9.7 16 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 wapele ct M exhibit_6.5.jpg 507x1,319 pixels 6 Home 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 4122 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