A small market research firm has to conduct surveys for three of their major clients (Superbikes and Auto, Kim's Fruit Market and Natalia's Farm Machinery). The company employs four statisticians who can be assigned to these three projects. However, these employees are very busy and can therefore only handle one client each. Due to the different experience and ability of these statisticians, the time required (in hours) to finish each job will differ. The required times are shown in the table below:

	Client
Statistician	Superbikes & Auto	Kim's Fruit Market	Natalia's Farm Machinery
Monica	150	210	270
William	170	230	220
Felicity	180	230	225
Ross	160	240	230

Complete the following tasks:

(a) Formulate a linear programming model to optimise the use of the company's busy statisticians.

(b) Solve the problem as a tableau model by computer. Present and interpret the solution.

(c) Suppose that the time Ross needs to complete the job for Superbikes & Auto is increased from 160 to 165 hours. What effect will this have on the optimal solution?

(d) Suppose that the time Felicity needs to complete the job for Kim's Fruit Market increases to 250 hours. What effect will this change have on the solution?