A city council voted to conduct a study on inner-city community problems using sociologists and research assistants from a nearby university. Allocation of time and costs per week are given in the table. How many sociologists and how many research assistants should be hired to minimize the cost and meet the weekly labor-hour requirements? What is the minimum weekly cost?

In Problem construct a mathematical model in the form of a linear programming problem.

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Labor-Hours Minimum Labor-Hours Needed per Research Sociologist Assistant Fieldwork Research center Costs per week 10 30 $500 Week 180 140 30 10 $300