Problem:
linear programming model
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 who 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.
Client
Statistician A 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 increased to 250 hours. What effect will this change have on the solution?