Q$2.$ An electronics company is considering which research and development projects to select. The following are the resource requirements and the estimated profit for each project:

$\backslash$table$[[$Project$,$Expense $($$$),$Scientists Required,Estimated Profit $($$$)],[1,70,000,7,360,000],[2,110,000,9,820,000],[3,50,000,8,290,000],[4,45,000,4,160,000],[5,90,000,7,560,000],[6,85,000,6,610,000],[7,70,000,8,480,000],[8,65,000,5,410,000]]$

The number of available scientists is $40$ and the budget available for these research and development projects is $$300,000.$

Furthermore, if project $2$ is selected, project $5$ must also be selected $($but not vice versa$).$ Projects $3$ and $4|$ are mutually exclusive $($both cannot be selected$).$

Formulate an integer programming model to determine which projects should be selected to maximize profit.