BMAD 65 Posted May 14, 2013 Report Share Posted May 14, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. 1 1 Quote Link to post Share on other sites

0 Solution bushindo 14 Posted May 14, 2013 Solution Report Share Posted May 14, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. 1 Quote Link to post Share on other sites

0 BMAD 65 Posted May 15, 2013 Author Report Share Posted May 15, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. How many days does each person contribute to the total project days? Quote Link to post Share on other sites

0 bonanova 85 Posted May 16, 2013 Report Share Posted May 16, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. How many days does each person contribute to the total project days? Individuals don't contribute to the project's time. A can do a project, alone, in a days, but a does not increase the time of a project. Rather, 1/a contributes to the reciprocal of the project's time. 1/a +1/b+1/c = 1/10, etc. Quote Link to post Share on other sites

0 BMAD 65 Posted May 16, 2013 Author Report Share Posted May 16, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. How many days does each person contribute to the total project days? Individuals don't contribute to the project's time.A can do a project, alone, in a days, but a does not increase the time of a project.Rather, 1/a contributes to the reciprocal of the project's time. 1/a +1/b+1/c = 1/10, etc. Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects. Quote Link to post Share on other sites

0 ShadowAngel7 0 Posted May 17, 2013 Report Share Posted May 17, 2013 (edited) Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.Together, A, B, and C can complete it in 10 days.Together, B, C, and D can complete it in 11 days.Together, C, D, and A can complete it in 12 days.Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. How many days does each person contribute to the total project days? Individuals don't contribute to the project's time.A can do a project, alone, in a days, but a does not increase the time of a project.Rather, 1/a contributes to the reciprocal of the project's time. 1/a +1/b+1/c = 1/10, etc.Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects.So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive. Edited May 17, 2013 by ShadowAngel7 Quote Link to post Share on other sites

0 BMAD 65 Posted May 17, 2013 Author Report Share Posted May 17, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. How many days does each person contribute to the total project days? Individuals don't contribute to the project's time.A can do a project, alone, in a days, but a does not increase the time of a project.Rather, 1/a contributes to the reciprocal of the project's time. 1/a +1/b+1/c = 1/10, etc. Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects. So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive. essentially, i am asking how much of the duration is caused by each individual on the three man team if we assume that a person is just as productive no matter who they work with Quote Link to post Share on other sites

0 bushindo 14 Posted May 17, 2013 Report Share Posted May 17, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. How many days does each person contribute to the total project days? Individuals don't contribute to the project's time.A can do a project, alone, in a days, but a does not increase the time of a project.Rather, 1/a contributes to the reciprocal of the project's time. 1/a +1/b+1/c = 1/10, etc. Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects. So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive. essentially, i am asking how much of the duration is caused by each individual on the three man team if we assume that a person is just as productive no matter who they work with Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively. It is straightforward to construct a linear equation Bx = y where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively. [1,] 0.02614608 [2,] 0.03372183 [3,] 0.04013209 [4,] 0.01705517 Units are project/day. From here, it is simple to compute how much each individual contributes to a project. Quote Link to post Share on other sites

0 BMAD 65 Posted May 17, 2013 Author Report Share Posted May 17, 2013 Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project. Together, A, B, and C can complete it in 10 days. Together, B, C, and D can complete it in 11 days. Together, C, D, and A can complete it in 12 days. Together, D, A, and B can complete it in 13 days. Who is the best performer? Prove your answer. In each scenario, 1 worker is excluded and everyone else contributes. Therefore the best worker is the one without whom the work takes the longest. That would mean C is the best worker since without him it takes 13 days to complete the task. How many days does each person contribute to the total project days? Individuals don't contribute to the project's time.A can do a project, alone, in a days, but a does not increase the time of a project.Rather, 1/a contributes to the reciprocal of the project's time. 1/a +1/b+1/c = 1/10, etc. Allow me to rephrase cause I disagree: Including someone on a project and excluding someone else directly affects the amount of days a project takes. So in terms of making a three man team we can determine the day load attributed to each person (as well as rank them by productivity). In terms of proportional pay for effectiveness this is very important as we in manufacturing projects pay individuals incentives based on their individual contribution to group projects. So, by your later question, are you asking for how long each individual would take to complete the project working on his/her own? [edit from here] This would then, of course, make that proportional payment easier, using [actual time]/[individual time] to determine the proportion of total payment each individual should receive. essentially, i am asking how much of the duration is caused by each individual on the three man team if we assume that a person is just as productive no matter who they work with Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively. It is straightforward to construct a linear equation Bx = y where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively. [1,] 0.02614608 [2,] 0.03372183 [3,] 0.04013209 [4,] 0.01705517 Units are project/day. From here, it is simple to compute how much each individual contributes to a project. I like your answer. It is interesting how in America this problem is solved differently from my home country. Quote Link to post Share on other sites

0 bushindo 14 Posted May 17, 2013 Report Share Posted May 17, 2013 Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively. It is straightforward to construct a linear equation Bx = y where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively. [1,] 0.02614608 [2,] 0.03372183 [3,] 0.04013209 [4,] 0.01705517 Units are project/day. From here, it is simple to compute how much each individual contributes to a project. I like your answer. It is interesting how in America this problem is solved differently from my home country. I'm intrigued. How do people from your country solve this problem? Quote Link to post Share on other sites

0 BMAD 65 Posted May 17, 2013 Author Report Share Posted May 17, 2013 Let a, b, c, and d stand for the fraction of a project that A, B, C, and D can do within each day, respectively. It is straightforward to construct a linear equation Bx = y where B is a 4x4 matrix given from the OP, and y = (1,1,1,1)'. Solving for x, we get the following values for A, B, C, and D, respectively. [1,] 0.02614608 [2,] 0.03372183 [3,] 0.04013209 [4,] 0.01705517 Units are project/day. From here, it is simple to compute how much each individual contributes to a project. I like your answer. It is interesting how in America this problem is solved differently from my home country. I'm intrigued. How do people from your country solve this problem? 1 1 Quote Link to post Share on other sites

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## BMAD 65

Anna (A), BIll (B), Cindy ©, and Dante (D) work on a project.

Together, A, B, and C can complete it in 10 days.

Together, B, C, and D can complete it in 11 days.

Together, C, D, and A can complete it in 12 days.

Together, D, A, and B can complete it in 13 days.

Who is the best performer? Prove your answer.

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