A developer of video game software has seven proposals for new games. Unfortunately, the company cannot develop all the proposals because its budget for new projects is limited to $5950,000$ and it has only $20$

programmers to assign to new projects. The financial requirements, returns, and the number of programmers required py ach prbject are summarized in the following table. Projects $2$ and $6$ require specialized

programming knowledge that only one of the programmers has. Both of these projects To exit full screen: press and hald Escrammer with the necessary skills can be assigned to anly one of the projects. $($Note: All

dollar amounts represent thousands.$)$

$($a$)$ Formulate an ILP model for this problem to maximize NPV $($in thousands of dollars$).($Let $x_i=1$ if project $j$ is selected and $0$ otherwise. In your projects $2$ and $6$ constraint, only use coefficients of $1$ or $-1.)$

MAx :

Subject to:

total programmers constraint

budgetary constraint

projects $2$ and $6$ constraint

$x_i$ binary

$($b$)$ Create a spreadsheet model for this problem and solve it$.$ What is the optimal solution?