$(10$ points$)$ A farmer mills his own cattle feed and has the following information.

$\backslash$table$[[,$Corn,Hay,Soybeans,Salt,Vitamin A$],[$Cost$,5\mathrm{.}25,1\mathrm{.}25,11,25,20],[$Protein$,1\mathrm{.}75,2,5\mathrm{.}5,0,0],[$Fat$,0\mathrm{.}35,0\mathrm{.}05,0\mathrm{.}15,0,0],[$Salt$,0\mathrm{.}01,0,0\mathrm{.}01,1,0],[$Vitamin A$,0,0,0,0,1],[$Energy$,1\mathrm{.}5,0\mathrm{.}5,1\mathrm{.}25,0,0]]$

He wants to create the lowest cost feed with the following requirements: protein is between $1500$ and $3000$ units, fat is between $20$ and $40$ units, salt is at least $100$ units, vitamin A is at least $20$ units, and energy is at least $250$ units.

a$)$ What is the standard format? $(2$ pts$)$

b$)$ What will be his optimal feed mix? What will be his cost? $(2$ pts$)$

c$)$ What does the price of soybeans need to be before he includes it$?$ Why? $(2$ pts$)$

d$)$ What is the shadow price of salt? What does this mean? $(2$ pts$)$