table:

Formulate an integer program that maximizes Tower's profit $($in millions of dollars$)$ subject to the following management constraints:

Use no more than $180$ engineers.

Use no more than $155$ support personnel.

If either project $6$ or project $2$ is done, both must be done.

Project $5$ can be done only if project $4$ is done.

If project $3$ is done, project $1$ must not be done and vice versa.

No more than three projects are to be done.

Let $P_i=1$ if project $i$ is selected; $0$ otherwise.

Max

s$.$t$.$

constraint $1$

constraint $2$

constraint $3$

constraint $4$

constraint $5$

constraint $6$

$P_i=0,1$