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.

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 thesolution?

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Client Statistician 150 170 180 160 210 230 230 240 270 220 225 230