$\backslash$table$[[$PROBLEM $1$ Optimization $(50$ points$),,,],[,,,],[$Alocal farmer,,,$]]$

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 is busy preparing his production plan for next year. His problem is that of deciding what to grow; alfal corn or soy beans or a combination of those. One ton of alfalfa takes $0\mathrm{.}35$ acres of land, $0\mathrm{.}75$ acre$/$ft 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$/$ft of water and nets $$28.$

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

Answer the following questions and DEFEND YOUR ANSWERS:

b$)$ If the profit of corn increase to $$30$ per ton will Jerry produce any com? Is the overall profit going

c$)$ If only $1000$ acres of land was available would his profit remain the same? Explain.

d$)$ Jerry has option of increasing his allotted $2000$ acre$-$feet to $2200$ acre$-$feet at a price of $$33$ per ac