The Corner Coffee Shop blends and sells three basic blends in $1$ lb$.$ bags SpecialMountain Dark and Mill RegularIt uses four different types of coffee to produce the blends $-$ Brazilian mocha, Colombian and mild $.$ The shop has the following blend recipe requirements : Blend Mix Requirements Selling Price$/$Pound Special Dark $56\mathrm{.}50$ At least $40$Columbian, at least $30$ mocha At least $60\%$ Brazilian, no more than $10\%$ mild No more than $60$mild $,$ at least $305\mathrm{.}253\mathrm{.}75$ The cost of Brazilian coffee is $$2\mathrm{.}00$ per lb$.$the cost of mocha is $$2\mathrm{.}75$ per lb$.$the cost of Colombian is $$2\mathrm{.}00$ per lb$.$and the cost of mild is $$1\mathrm{.}75$ per lb$.$ The shop has $110$ lbs$.$ of Brazilian coffee, $70$ lbsof mocha, $80$ lbs of Colombian and $150$ lbs$.$ of mild coffee available each week. The shop wants to know the amount of each blend Special Dark, and to prepare each week to maximize profit. The linear programming model for this problem isas follows: X $||=$lbs$.$ of coffee used in blend per week, where i $=$ b $($Brazilian $),$ o $($Mocha$),$ c $($ Colombian $)$ m $($mild$),$ and j $=$ s $($ special$),$ d $($dark$),$ and r $($regular$)$