The research center has 10 researchers, each of whom can work on at most 2 projects. Six projects are under consideration. Each project requires 4 researchers. The required researchers (the staff ID) and the revenue of each project is shown in the table below: Projects 2 3 4 5 6 Required Researchers 1,4,5,8 2,3,7,10 1,6,8,9 2,3,5,10 1,6,7,9 2,4,8,10 Revenue ($) 12.000 11.000 16.000 8.000 9,000 13.000 1 Each researcher who is used on at least one project must be paid the fee in the table below. This is a one-time payment. That is, even if that researcher is used on two projects, he or she will only be paid once. Researcher ID 1 2 5 6 7 8 910 Fee (S) 300 500 700 400 800 500 800 3 4 600 400 900 Maximize the research center's net profit using integer programming. The decision variables x; and y; are defined. x;= 1 , if the researcher i is used and otherwise (i=1...,10) y:=1 , if project j is undertaken and otherwise (j=1__,6) Your task: Formulate the linear programming problem 1. Objective Function 2. Constraints| Each of researcher can work on at most 2 projects - If a project is undertaken, then all the 4 researchers required are used. The research center has 10 researchers, each of whom can work on at most 2 projects. Six projects are under consideration. Each project requires 4 researchers. The required researchers (the staff ID) and the revenue of each project is shown in the table below: Projects 2 3 4 5 6 Required Researchers 1,4,5,8 2,3,7,10 1,6,8,9 2,3,5,10 1,6,7,9 2,4,8,10 Revenue ($) 12.000 11.000 16.000 8.000 9,000 13.000 1 Each researcher who is used on at least one project must be paid the fee in the table below. This is a one-time payment. That is, even if that researcher is used on two projects, he or she will only be paid once. Researcher ID 1 2 5 6 7 8 910 Fee (S) 300 500 700 400 800 500 800 3 4 600 400 900 Maximize the research center's net profit using integer programming. The decision variables x; and y; are defined. x;= 1 , if the researcher i is used and otherwise (i=1...,10) y:=1 , if project j is undertaken and otherwise (j=1__,6) Your task: Formulate the linear programming problem 1. Objective Function 2. Constraints| Each of researcher can work on at most 2 projects - If a project is undertaken, then all the 4 researchers required are used