A market research firm's three clients each requested that the firm conduct a sample survey. Four available statisticians can be assigned to these three projects; however, all four statisticians are busy, and therefore each can handle only one client. The following data show the number of hours required for each statistician to complete each job; the differences in time are based on experience and ability of the statisticians.
|
Statistician
|
A
|
Client B
|
C
|
|
1
|
150
|
210
|
270
|
|
2
|
170
|
230
|
220
|
|
3
|
180
|
230
|
225
|
|
4
|
160
|
240
|
230
|
a. Formulate and solve a linear programming model for this problem.
b. Suppose that the time statistician 4 needs to complete the job for client A is increased from 160 to 165 hours. What effect will this change have on the solution?
c. Suppose that the time statistician 4 needs to complete the job for client A is decreased to 140 hours. What effect will this change have on the solution?
d. Suppose that the time statistician 3 needs to complete the job for client B increases to 250 hours. What effect will this change have on the solution?