Acertain academic department at a local university will conduct a research project. the department will need to hire graduate research assistants and professional researchers. each graduate research assistant will need to work 28 hours per week on fieldwork and 12 hours per week at the university's research center. each professional researcher will need to work 15 hours per week on fieldwork and 25 hours per week at the university's research center. the minimum number of hours needed per week for fieldwork is 170 and the minimum number of hours needed per week at the research center is 139. each research assistant will be paid $293 per week and each professional researcher will be paid $496 per week. let x denote the number of graduate research assistants hired and let y denote the number of professional researcher hired. the department wants to minimize cost. set up the linear programming problem for this situation.