Tower Engineering Corporation Is Considering Undertaking Several Proposed Projects for the Next

Tower Engineering Corporation is considering undertaking several proposed projects for the next fiscal year. The projects, the number of engineers and the number of support personnel required for each project, and the expected profits for each project are summarized in the following table: $\begin{array}{lllllll}&&&\text { Project }\\&1&2&3&4&5&6\\\hline\text { Engineers Required } & 20 & 55 & 47 & 38 & 90 & 63 \\\text { Support Personnel Required } & 15 & 45 & 50 & 40 & 70 & 70 \\\text { Profit }(\$ 1,000,000 s) & 1.0 & 1.8 & 2.0 & 1.5 & 3.6 & 2.2\end{array}$ Formulate an integer program that maximizes Tower's profit subject to the following management constraints:
1)
Use no more than 175 engineers
2)
Use no more than 150 support personnel
3)
If either project 6 or project 4 is done, both must be done
4)
Project 2 can be done only if project 1 is done
5)
If project 5 is done, project 3 must not be done and vice versa
6)
No more than three projects are to be done.