A market research firm has three clients who have each requested that the firm conduct a sample survey. Four statisticians are available to assign to these three projects: However, all four statisticians are busy, and therefore each can handle at most one of the clients. The following data show the number of hours, it would take for each statistician to complete each job, the differences in time are due to differences in experience and ability among the statisticians. Statistician Client A B C 1 150 210 270 2 170 230 220 3 180 230 225 4 160 240 230 a) Formulate a linear programming (LP) model for this problem. b) Use solver to find the optimal assignment rule c) Suppose that the time it takes statistician 4 to complete the job for client A is decreased to 140 hours. What effect will this have on the solution. d) As a management science student, the Managing Director of the e) Company seeks your expert advice on ways in which to determine the optimal assignment rule. Advise the MD, providing detailed explanation using your answer obtain in (b). Write your answer in a form of a report to the MD.
Question 2
A market research firm has three clients who have each requested that the
firm conduct a sample survey. Four statisticians are available to assign to
these three projects: However, all four statisticians are busy, and therefore
each can handle at most one of the clients. The following data show the
number of hours, it would take for each statistician to complete each job,
the differences in time are due to differences in experience and ability
among the statisticians.
| Statistician | Client | ||
| A | B | C | |
| 1 | 150 | 210 | 270 |
| 2 | 170 | 230 | 220 |
| 3 | 180 | 230 | 225 |
| 4 | 160 | 240 | 230 |
a) Formulate a linear programming (LP) model for this problem.
b) Use solver to find the optimal assignment rule
c) Suppose that the time it takes statistician 4 to complete the job for
client A is decreased to 140 hours. What effect will this have on the
solution.
d) As a management science student, the Managing Director of the
e) Company seeks your expert advice on ways in which to determine the
optimal assignment rule. Advise the MD, providing detailed explanation
using your answer obtain in (b). Write your answer in a form of a report
to the MD.
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