Problem H$2(10\%)$: A coffee blender receives $1000$ kg of Grade A coffee, $2000$ kg of Grade B$,$ and $3000$ kg of Grade

C coffee per week. The blender purchases Gndes $A,B,$ and $in$ for $$\frac{10}{k}g.\frac{56}{k}g$ and $$\frac{4}{k}g$ respectively. The coffee

blender produced $3$ blend types: exotic $($E$)$; supreme $($ S $),$ and regular $($R$).$ It ean sell blend E$,$ which consists of $40\%$

Grade A$,50\%$ Grade B$,$ and $10\%$ Grade C$,$ for $$\frac{20}{k}g,$ that requires $$\frac{5}{k}g$ in processing cost. It can sell blend $S,$

which consists of $25\%$ Grade A$,50\%$ Grade B$,$ and $25\%$ Grade C for $$\frac{15}{k}g$ that requires $$\frac{3}{k}g$ in processing cost.

It can sell blend $R,$ which consists of $10\%$ Grade A$,30\%$ Grade B$,$ and $60\%$ Grade C$,$ for $$\frac{10}{k}g$ that requires $$\frac{2}{k}g$

in processing cost. The demand for blend $R$ is at least $3000k\frac{g}{?}$ week, where the demand for blends $E$ and $S$ do niot

exceed $1000k\frac{g}{?}$ week and $2000k\frac{g}{?}$ week respectively. Formulate this as a linear programming$-$problem to maximize

the blender profit function. $($Cest lo $$)$