Hill$-$O$-$Beans Coffee Company blends four component beans into three final blends of coffee: One is sold to luxury hotels, another to restaurants and the third to supermarkets for store$-$label brands. The company has four reliable bean supplies: $$ rgentine $$ bundo, Peruvian Colmado, Brazilian Maximo and Chilean Saboro. The table below summarizes the very precise recipes for the final coffee blends, the cost and availability information for the four components and the wholesale price per pound of the final blends. The percentages indicate the fraction of each component to be used in each blend.

$\backslash$table$[[$Component$,$Hotel,Restaurant,Market,Cost$/$Pound$,$Weekly $$ vailability$],[$Abundo$,20\%,35\%,10\%,0\mathrm{.}60,40,000],[$Colmado$,40\%,15\%,35\%,0\mathrm{.}80,25,000],[$Maximo$,15\%,20\%,40\%,0\mathrm{.}55,20,000],[$Saboro$,25\%,30\%,15\%,0\mathrm{.}70,45,000],[$Wholesale price$/$pound$,1\mathrm{.}25,1\mathrm{.}50,1\mathrm{.}40,,]]$

The processor's plant can handle no more than $100,000$ pounds per week and Hill$-$O$-$Beans would like to operate at capacity. There is no problem in selling the final blends although the marketing department requires minimum production levels of $10,000,25,000$ and $30,000$ pounds respectively for the hotel, restaurant and market blends.

Write a linear program to maximize the weekly profit of Hill$-$O$-$Beans. Make sure to explicitly define all decision variables.