$13-14.$ Three alternatives are being considered for an engineering project. Their cash$-$flow estimates are shown in the accompanying table. A and B are mutually exclusive, and C is an optional add$-$on feature to alternative A$.$ Investment funds are limited to $$5,000,000.$ Another constraint on this project is the engineering personnel needed to design and implement the solution. No more than $10,000$ person$-$hours of engineering time can be committed to the project. Set up a linear integer PROBLEMS $625$ programming formulation of this resource allocation problem. $(13\mathrm{.}9)$ Alternative ABC Initial investment $($$$106)4\mathrm{.}04\mathrm{.}51\mathrm{.}0$ Personnel requirement $7,0009,0003,000($hours$)$ Alternative AB C After$-$tax annual $1\mathrm{.}32\mathrm{.}20\mathrm{.}9$ savings, years one through four $($$$106)$ PW at $10\%$ per year $0\mathrm{.}122\mathrm{.}471\mathrm{.}85$