Question: A market research firm has three clients who have each requested that the firm conducts a sample survey. Four available statisticians can be assigned to these three projects: how. ever. all four statisticians are busy. and therefore each can handle only one of the clients 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.

1. Formulate and solve a linear programming model for this problem.
2. Suppose that the time it takes statistician 4 to complete the job for client \(\mathrm{A}\) is increased from 160 to 165 hours. What effect will this change have on the solution?
3. Suppose that the time it takes statistician 4 to complete the job for client \(\mathrm{A}\) is decreased to 140 hours. What effect will this change have on the solution?
4. Suppose that the time it takes statistician 3 to complete the job for client B increases to 250 hours. What effect will this change have on the solution?

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