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:

Projects

$123456$

Engineers Required $205547389063$

Support Personnel Required $154550407070$

Profit $($$$1,000,000$s$)1\mathrm{.}01\mathrm{.}82\mathrm{.}01\mathrm{.}53\mathrm{.}62\mathrm{.}2$

Formulate an integer program that maximizes Tower's profit subject to the management constraints, which are listed below.

$(2$ points$)$ Define the decision variables:

$(1$ point$)$ Write the objective function:

$(7$ points; one point each$)$ Write constraints for the following requirements: