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$1$ PROBLEM $1$ Optimization $(50$ points$)$

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A local farmer, Jerry Glover, operates a $1200-$acre irrigated farm in rural Water District No$.6.$ District Authority has just given its water allotments for the next year $($Jerry was allotted $2000$ acre$-$feet$)$ and Jerry is busy preparing his production plan for next year. His problem is that of deciding what to grow; alfalfa, corn or soy beans or a combination of those. One ton of alfalfa takes $0\mathrm{.}35$ acres of land, $0\mathrm{.}75$ acre$/$t of water and will bring an expected profit of $$24.$ One ton of corn takes $0\mathrm{.}2$ acres of land, $0\mathrm{.}90$ acre$/$ft of water and nets $$20.$ One ton of soy beans takes $0\mathrm{.}3$ acres of land, $0\mathrm{.}8$ acre$/$t of water and nets $$28.$

Formulate Jerry's production problem as the linear programming optimization problem:

Answer the following questions and DEFEND YOUR ANSWERS:

$\backslash$table$[[,$alfaalfa,corn,Soy$],[$land$,0\mathrm{.}35,0\mathrm{.}2,0\mathrm{.}3],[$water$,0\mathrm{.}75,0\mathrm{.}9,0\mathrm{.}8],[$nets$,$$$24\mathrm{.}00,$$$20\mathrm{.}00,$$$28\mathrm{.}00$