Q$35.($Capital Budgeting$)$ Tower Engineering Corporation is considering undertaking three proposed projects for the next fiscal year. The projects, the number of engineers and support personnel required for each project, and the expected profits for each project are summarized in the following table:

$$

Project $1$

Project $2$

Project $3$

Engineers required

$32$

$35$

$36$

Support personnel required

$35$

$40$

$50$

Profit $($$million$)$

$2$

$2\mathrm{.}4$

$3$

$$

Formulate an integer program that maximizes Tower's profit subject to the following management constraints. Use X$1,$ X$2$ and X$3=1$ or $0$ to express whether the project is selected or not. Use no more than $75$ engineers and no more than $80$ support personnel. $(5$