3. The manufacturing process at Lone Star Company (LSC) is following a 70% learn

Question

3. The manufacturing process at Lone Star Company (LSC) is following a 70% learning curve. More recently, the company produced four conveyors with the last one requiring 490 labor hours to complete (i.e., P4 = 490). LSC 2 has received an invitation to bid on an order of two additional conveyors. Based on the tables at the end of Chapter 11, what is the total amount of time required to make the fifth and the sixth conveyors?

[Hint: Try to find A first by recalling that each time the output level doubles (from 1 unit to 2 units, from 2 units to 4 units, etc.), the number of labor hours required to complete a task decreases to a fixed percentage of its previous time requirement.]  

Learning Curve Table attached

70% 75% 80% 85% 90% Unit Unit Total Unit Total Unit Total Unit Total Unit Total Number Time Time Time Time Time Time Time Time Time Time 11.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 700 1.700750 1.750 8001.800 8501.850900 1.900 568 2.268 634 2.384 702 2.502 773 2.623 846 2.746 490 2.758 .562 2.946 640 3.142 723 3.345 810 3.556 437 3.195 513 3.459 596 3.738 686 4.0317834.339 398 3.593 475 3.934 562 4.299 657 4.688 762 5.101 367 3.960446 4.380534 4.834634 5.322 744 5.845 343 4.303 422 4.802 .512 5.346 614 5.936 7296.574 323 4.626 402 5.204 493 5.839 597 6.533 716 7.290 306 4.932 385 5.589 4776.315 583 7.116705 7.994 291 5.223 370 5.958 4626.777570 7.686695 8.689 278 5.501 357 6.315 4497.227 558 8.244 685 9.374 2675.769 345 6.660 4387.665 548 8.792 677 10.052 257 6.026 334 6.994 428 8.092 539 9.331670 10.721 248 6.274 325 7.319 418 8.511 530 9.861 663 11.384 240 6.514 316 7.635 410 8.920 522 10.383 656 12.040 233 6.747 309 7.944 402 9.322 515 10.898 650 12.690 226 6.973 301 8.245 394 9.716 508 11.405644 13.334 220 7.192 295 8.540 388 10.104501 11.907 639 13.974 214 7407 288 8.828 381 10.485 495 12.402 634 14.608 209 7.615 283 9.111 375 10.860 490 12.892630 15.237 204 7.819 277 9.388 370 11.230 484 13.376 625 15.862 199 8.018 272 9.660 364 11.594 479 13.856 621 16.483 195 8.213 267 9.928 359 11.954 475 14.331 617 17.100 191 8.404 263 10.191 355 12.309 470 4.80613 17.713 187 8.591 259 10.449 350 12.659466 15.267 609 18.323 183 8.774 255 10.704 346 13.005 462 15.728606 18.929 180 8.954 251 10.955 342 13.347 458 16.186 603 19.531 177 9.131 247 11.202 338 13.685 454 16.640 599 20.131 174 9.305 24411.446 335 14.020 450 17.091 596 20.727 10 12 13 14 16 19 21 23 24 25 26 27 28 29 30

Explanation / Answer

Learning factor = ln 0.7/ln 2 = -0.5145

Timr required to complete 4th unit = Time required to complete first unit * (4 to power of learning factor)
490 = Time required to complete first unit *(4^-0.5145)
Time required to complete first unit = 999.9 hours = 1000 hours

Time required to complete 5th unit = 1000*(5^-0.5145)= 436.9 ~ 437 hours
Time required to complete 6th unit = 1000*(6^-0.5145)= 397.8 ~ 398 hours

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