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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 developme 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 5 6 7 8 9 10 COST ($ MILLIONS) $ 12 10 6.0 6.5 5.8 Learning rate 6.0 5.0 3.6 3.6 4.1 UNIT COST NUMBER ($ MILLIONS) 11 Cost for 120 more units 12 13 14 15 Expected cost for last unit 16 17 18 19 20 a. Based on past experience, what is the learning rate? (Do not round Intermediate calculations. Round your answer to the nearest whole percent.) $3.9 3.5 3.0 2.8 2.7 2.7 2.3 % 3.0 2.9 2.6 b. What cost should LTI use in their bid for the total order of 100 additional units, assuming that learning continues? c. What is the cost expected to be for the last unit under the learning rate you estimated?

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 developme 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 5 6 7 8 9 10 COST ($ MILLIONS) $ 12 10 6.0 6.5 5.8 Learning rate 6.0 5.0 3.6 3.6 4.1 UNIT COST NUMBER ($ MILLIONS) 11 Cost for 120 more units 12 13 14 15 Expected cost for last unit 16 17 18 19 20 a. Based on past experience, what is the learning rate? (Do not round Intermediate calculations. Round your answer to the nearest whole percent.) $3.9 3.5 3.0 2.8 2.7 2.7 2.3 % 3.0 2.9 2.6 b. What cost should LTI use in their bid for the total order of 100 additional units, assuming that learning continues? c. What is the cost expected to be for the last unit under the learning rate you estimated?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Ch. 6 Q6
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 easler 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 5 6 7 8 9 10 COST ($ MILLIONS) $12 Learning rate 10 6.0 6.5 5.8 6.0 5.0 3.6 3.6 4.1 a. Based on past experience, what is the learning rate? (Do not round Intermediate calculations. Round your answer to the nearest whole percent.) UNIT COST NUMBER ($ MILLIONS) 11 12 13 14 15 16 17 18 19 20 Cost for 120 more units $3.9 3.5 3.0 2.8 2.7 2.7 2.3 3.0 2.9 2.6 % b. What cost should LTI use in their bid for the total order of 100 additional units, assuming that learning continues? Expected cost for last unit c. What is the cost expected to be for the last unit under the learning rate you estimated?
Transcribed Image Text:Lazer Technologies Inc. (LTI) has produced a total of 20 high-power laser systems that could be used to destroy any approaching enemy missiles or aircraft. The 20 units have been produced, funded in part as private research within the research and development arm of LTI, but the bulk of the funding came from a contract with the U.S. Department of Defense (DoD). Testing of the laser units has shown that they are effective defense weapons, and if redesigned to add portability and easler field maintenance, the units could be truck-mounted. The DoD has asked LTI to submit a bid for 100 more units. The 20 units that LTI has built so far cost the following amounts and are listed in the order in which they were produced: Use Exhibit 6.4 and Exhibit 6.5. UNIT NUMBER 1 2 3 4 5 6 7 8 9 10 COST ($ MILLIONS) $12 Learning rate 10 6.0 6.5 5.8 6.0 5.0 3.6 3.6 4.1 a. Based on past experience, what is the learning rate? (Do not round Intermediate calculations. Round your answer to the nearest whole percent.) UNIT COST NUMBER ($ MILLIONS) 11 12 13 14 15 16 17 18 19 20 Cost for 120 more units $3.9 3.5 3.0 2.8 2.7 2.7 2.3 3.0 2.9 2.6 % b. What cost should LTI use in their bid for the total order of 100 additional units, assuming that learning continues? Expected cost for last unit c. What is the cost expected to be for the last unit under the learning rate you estimated?
Exhibit 6.4 Unit 1 2 3 4 5 6 7 8 Unit Improvement Factor 60% 70% 65% 1.0000 1.0000 1,0000 6000 6500 7000 4450 5052 5682 3600 4225 4900 3054 3678 4368 2670 3284 3977 2383 2984 3674 2160 2746 3430 1980 2552 3228 1832 2391 3058 1602 2135 2784 1430 1940 2572 1290 1785 2401 1188 1659 2260 1099 1554 2141 1025 1465 2038 0961 1387 1949 0933 1353 1908 0815 1208 1737 0728 1097 1605 0660 0605 0560 0489 0437 0396 0363 0336 0294 0262 0237 0218 0201 0171 0149 0133 0121 0111 0103 0090 9 10 12 14 16 18 20 22 24 25 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 250 300 350 400 450 500 600 700 800 900 1,000 1,200 1,400 1,600 1,800 2,000 2,500 3,000 Improvement Curves: Table of Unit Values 0080 0073 0067 0062 0054 0048 0044 0040 0037 0031 0027 1010 0939 0879 0785 0713 0657 0610 0572 0510 0464 0427 0397 0371 0323 0289 0262 0241 0224 0210 0188 0171 0157 0146 0137 0122 0111 0102 0095 0089 0077 0069 1498 1410 1336 1216 1123 1049 0987 0935 0851 0786 0734 0691 0655 0584 0531 0491 0458 0431 0408 0372 0344 0321 0302 0286 0260 0240 0225 0211 0200 0178 0162 75% 1.0000 7500 6338 5625 5127 4754 4459 4219 4017 3846 3565 3344 3164 3013 2884 2772 2674 2629 2437 2286 2163 2060 1972 1828 1715 1622 1545 1479 1371 1287 1217 1159 1109 1011 0937 0879 0832 80% 1.0000 8000 7021 6400 0427 0389 0360 5956 5617 5345 5120 4930 4765 4493 4276 4096 3944 3812 3697 3595 3548 3346 3184 .3050 2936 2838 2676 2547 2440 2349 2271 2141 2038 1952 1879 1816 85% 1.0000 8500 7729 7225 6857 .6570 6337 6141 1691 1594 1517 1453 0792 1399 0758 1352 0703 1275 0659 1214 0624 1163 0594 1119 0569 1082 0527 1020 0971 0495 0468 0930 0446 0895 0866 0806 0760 5974 5828 5584 5386 5220 5078 4954 4844 4747 4701 4505 4345 4211 4096 3996 3829 .3693 3579 3482 3397 3255 3139 3042 2959 2887 2740 2625 2532 2454 2387 2329 2232 2152 2086 2029 1980 1897 1830 1773 1725 1683 1597 1530 90% 1.0000 9000 8462 8100 7830 7616 7439 7290 7161 7047 6854 6696 6561 6445 6342 6251 6169 6131 5963 5825 5708 5607 5518 5367 5243 5137 5046 4966 4830 4718 4623 4541 4469 4320 4202 4105 4022 3951 3888 3782 3694 3620 3556 3499 3404 3325 3258 3200 3149 3044 2961 O 95% 1.0000 9500 9219 9025 8877 8758 8659 8574 8499 8433 8320 8226 8145 8074 8012 7955 7904 7880 7775 7687 7611 7545 7486 7386 7302 7231 7168 7112 7017 6937 6869 6809 6757 6646 6557 6482 6419 6363 6314 6229 6158 6098 6045 5998 5918 5850 5793 P 5743 5698 5605 55:30 Unit 1 2 3 4 5 6 7 8 9 10 12 14 16 2222222 18. 20 24 25 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 250 300 350 400 450 500 600 700 800 900 Cumulative Improvement Factor 80% 70% 1.000 1.700 2.268 75% 1.000 1.750 65% 1.000 1.650 2045 2.155 2.578 2.405 2.758 2946 3.195 2.710 2.977 3.274 3.593 3572 3.960 4.303 3.847 4.626 4.102 4.341 4.931 4.780 5.501 5.177 6.026 5.541 6.514 6.972 5.879 6.195 7.407 6.492 7.819 6.773 8.213 3.216 3.432 3.630 3.813 4.144 4.438 4.704 4.946 5.171 5.379 6.909 8.404 1,000 1,200 1,400 60% 1.000 1.600 5.574 5.668 6.097 6.478 6.821 7.134 7.422 7.941 8401 8814 9.191 9.539 10.16 10.72 11.21 11.67 12.09 13.01 13.81 14.51 15.72 16.26 17.21 18.06 18.82 19.51 20.15 21.30 22.32 1,600 23.23 1,800 24.06 2,000 24.83 2.500 26.53 15.14 7.540 8.109 8.631 9.114 9.565 10.39 11.13 11.82 12.45 13.03 14.11 15.06 15.97 16.79 17.55 19.28 20.81 22.18 23.44 24.60 25.68 27.67 29.45 31.09 32.60 31.01 36.59 38.92 41.04 43.00 44.84 48.97 9.305 11.45 10.13 1272 10.90 13.72 11.62 1477 12.31 15.78 13.57 14.74 15.82 16.83 17.79 19.57 21.20 22.72 24.14 25.48 28.56 31.34 33.89 36.26 38.48 40.58 44.47 48.04 51.36 54.46 57.40 62.85 67.85 2.384 2946 3459 3.934 4.380 4.802 5.204 5.589 6315 6.994 7.635 8.245 8.828 9.388 9928 10.19 7249 76.85 80.96 90.39 17.67 1943 21.09 22.67 24.18 27.02 29.67 32.17 34.54 36 80 42.05 46.94 51.48 55.75 59.80 63.68 70.97 77.37 84.18 90.26 96.07 107.0 117.2 126.8 135.9 144.7 165.0 1.000 1.800 2.502 3.142 3.738 4.299 4834 5.346 5.839 6.315 7.227 8.092 8.920 9.716 10.48 11.23 11.95 12.31 14.02 15.64 17.19 18.68 20.12 22.87 25.47 27.96 30.35 32.65 37.05 41.22 45.20 49.03 52.72 61.47 69.66 77.43 84.85 91.97 98.85 112.0 124.4 136.3 1477 158.7 179.7 199.6 218.6 236.8 254.4 296.1 85% 1.000 1.850 2.623 3.345 4.031 4.688 5.322 5.936 6.533 7.116 8.244 9.331 10.38 11.41 12:40 13.38 14.33 14.80 17.09 19.29 21.43 23.50 25.51 29.41 33.17 36.80 40.32 43.75 50.39 56.78 62.95 68.95 74.79 88.83 102.2 115.1 127.6 139.7 151.5 174.2 196.1 217.3 237.9 257.9 296.6 3339 369.9 404.9 438.9 5208 90% 1.000 1.900 2.746 3.556 4.339 5.101 5.845 6.574 7.290 7.994 9.374 10.72 12.04 13.33 14.61 15.86 17.10 17.71 20.73 23.67 26.54 29.37 32.14 37.57 42.87 48.05 53.14 58.14 67.93 77.46 86.80 95.96 105.0 126.9 148.2 169.0 189.3 209.2 228.8 267.1 304.5 341.0 376.9 4122 481.2 5484 6142 678.8 7423 897.0 95% 1.000 1.950 2.872 3.774 4.662 5.538 6.404 7.261 8.111 8.955 10.62 12:27 13.91 15.52 17.13 18.72 20.31 21.10 25.00 28.86 32.68 36.47 40.22 47.65 54.99 62.25 69.45 76.59 90.71 104.7 118.5 132.1 145.7 179.2 212.2 244.8 277.0 309.0 340.6 403.3 465.3 526.5 587.2 647.4 766.6 884.2 1001 1116 1230 1513
Transcribed Image Text:Exhibit 6.4 Unit 1 2 3 4 5 6 7 8 Unit Improvement Factor 60% 70% 65% 1.0000 1.0000 1,0000 6000 6500 7000 4450 5052 5682 3600 4225 4900 3054 3678 4368 2670 3284 3977 2383 2984 3674 2160 2746 3430 1980 2552 3228 1832 2391 3058 1602 2135 2784 1430 1940 2572 1290 1785 2401 1188 1659 2260 1099 1554 2141 1025 1465 2038 0961 1387 1949 0933 1353 1908 0815 1208 1737 0728 1097 1605 0660 0605 0560 0489 0437 0396 0363 0336 0294 0262 0237 0218 0201 0171 0149 0133 0121 0111 0103 0090 9 10 12 14 16 18 20 22 24 25 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 250 300 350 400 450 500 600 700 800 900 1,000 1,200 1,400 1,600 1,800 2,000 2,500 3,000 Improvement Curves: Table of Unit Values 0080 0073 0067 0062 0054 0048 0044 0040 0037 0031 0027 1010 0939 0879 0785 0713 0657 0610 0572 0510 0464 0427 0397 0371 0323 0289 0262 0241 0224 0210 0188 0171 0157 0146 0137 0122 0111 0102 0095 0089 0077 0069 1498 1410 1336 1216 1123 1049 0987 0935 0851 0786 0734 0691 0655 0584 0531 0491 0458 0431 0408 0372 0344 0321 0302 0286 0260 0240 0225 0211 0200 0178 0162 75% 1.0000 7500 6338 5625 5127 4754 4459 4219 4017 3846 3565 3344 3164 3013 2884 2772 2674 2629 2437 2286 2163 2060 1972 1828 1715 1622 1545 1479 1371 1287 1217 1159 1109 1011 0937 0879 0832 80% 1.0000 8000 7021 6400 0427 0389 0360 5956 5617 5345 5120 4930 4765 4493 4276 4096 3944 3812 3697 3595 3548 3346 3184 .3050 2936 2838 2676 2547 2440 2349 2271 2141 2038 1952 1879 1816 85% 1.0000 8500 7729 7225 6857 .6570 6337 6141 1691 1594 1517 1453 0792 1399 0758 1352 0703 1275 0659 1214 0624 1163 0594 1119 0569 1082 0527 1020 0971 0495 0468 0930 0446 0895 0866 0806 0760 5974 5828 5584 5386 5220 5078 4954 4844 4747 4701 4505 4345 4211 4096 3996 3829 .3693 3579 3482 3397 3255 3139 3042 2959 2887 2740 2625 2532 2454 2387 2329 2232 2152 2086 2029 1980 1897 1830 1773 1725 1683 1597 1530 90% 1.0000 9000 8462 8100 7830 7616 7439 7290 7161 7047 6854 6696 6561 6445 6342 6251 6169 6131 5963 5825 5708 5607 5518 5367 5243 5137 5046 4966 4830 4718 4623 4541 4469 4320 4202 4105 4022 3951 3888 3782 3694 3620 3556 3499 3404 3325 3258 3200 3149 3044 2961 O 95% 1.0000 9500 9219 9025 8877 8758 8659 8574 8499 8433 8320 8226 8145 8074 8012 7955 7904 7880 7775 7687 7611 7545 7486 7386 7302 7231 7168 7112 7017 6937 6869 6809 6757 6646 6557 6482 6419 6363 6314 6229 6158 6098 6045 5998 5918 5850 5793 P 5743 5698 5605 55:30 Unit 1 2 3 4 5 6 7 8 9 10 12 14 16 2222222 18. 20 24 25 30 35 40 45 50 60 70 80 90 100 120 140 160 180 200 250 300 350 400 450 500 600 700 800 900 Cumulative Improvement Factor 80% 70% 1.000 1.700 2.268 75% 1.000 1.750 65% 1.000 1.650 2045 2.155 2.578 2.405 2.758 2946 3.195 2.710 2.977 3.274 3.593 3572 3.960 4.303 3.847 4.626 4.102 4.341 4.931 4.780 5.501 5.177 6.026 5.541 6.514 6.972 5.879 6.195 7.407 6.492 7.819 6.773 8.213 3.216 3.432 3.630 3.813 4.144 4.438 4.704 4.946 5.171 5.379 6.909 8.404 1,000 1,200 1,400 60% 1.000 1.600 5.574 5.668 6.097 6.478 6.821 7.134 7.422 7.941 8401 8814 9.191 9.539 10.16 10.72 11.21 11.67 12.09 13.01 13.81 14.51 15.72 16.26 17.21 18.06 18.82 19.51 20.15 21.30 22.32 1,600 23.23 1,800 24.06 2,000 24.83 2.500 26.53 15.14 7.540 8.109 8.631 9.114 9.565 10.39 11.13 11.82 12.45 13.03 14.11 15.06 15.97 16.79 17.55 19.28 20.81 22.18 23.44 24.60 25.68 27.67 29.45 31.09 32.60 31.01 36.59 38.92 41.04 43.00 44.84 48.97 9.305 11.45 10.13 1272 10.90 13.72 11.62 1477 12.31 15.78 13.57 14.74 15.82 16.83 17.79 19.57 21.20 22.72 24.14 25.48 28.56 31.34 33.89 36.26 38.48 40.58 44.47 48.04 51.36 54.46 57.40 62.85 67.85 2.384 2946 3459 3.934 4.380 4.802 5.204 5.589 6315 6.994 7.635 8.245 8.828 9.388 9928 10.19 7249 76.85 80.96 90.39 17.67 1943 21.09 22.67 24.18 27.02 29.67 32.17 34.54 36 80 42.05 46.94 51.48 55.75 59.80 63.68 70.97 77.37 84.18 90.26 96.07 107.0 117.2 126.8 135.9 144.7 165.0 1.000 1.800 2.502 3.142 3.738 4.299 4834 5.346 5.839 6.315 7.227 8.092 8.920 9.716 10.48 11.23 11.95 12.31 14.02 15.64 17.19 18.68 20.12 22.87 25.47 27.96 30.35 32.65 37.05 41.22 45.20 49.03 52.72 61.47 69.66 77.43 84.85 91.97 98.85 112.0 124.4 136.3 1477 158.7 179.7 199.6 218.6 236.8 254.4 296.1 85% 1.000 1.850 2.623 3.345 4.031 4.688 5.322 5.936 6.533 7.116 8.244 9.331 10.38 11.41 12:40 13.38 14.33 14.80 17.09 19.29 21.43 23.50 25.51 29.41 33.17 36.80 40.32 43.75 50.39 56.78 62.95 68.95 74.79 88.83 102.2 115.1 127.6 139.7 151.5 174.2 196.1 217.3 237.9 257.9 296.6 3339 369.9 404.9 438.9 5208 90% 1.000 1.900 2.746 3.556 4.339 5.101 5.845 6.574 7.290 7.994 9.374 10.72 12.04 13.33 14.61 15.86 17.10 17.71 20.73 23.67 26.54 29.37 32.14 37.57 42.87 48.05 53.14 58.14 67.93 77.46 86.80 95.96 105.0 126.9 148.2 169.0 189.3 209.2 228.8 267.1 304.5 341.0 376.9 4122 481.2 5484 6142 678.8 7423 897.0 95% 1.000 1.950 2.872 3.774 4.662 5.538 6.404 7.261 8.111 8.955 10.62 12:27 13.91 15.52 17.13 18.72 20.31 21.10 25.00 28.86 32.68 36.47 40.22 47.65 54.99 62.25 69.45 76.59 90.71 104.7 118.5 132.1 145.7 179.2 212.2 244.8 277.0 309.0 340.6 403.3 465.3 526.5 587.2 647.4 766.6 884.2 1001 1116 1230 1513
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