Coffee Bean Machine $($M$1)$ Machine $($M$2)$ Machine $($M$3)$ Profit per kg

B$130$ TBD TBD $6$

B$215$ TBD TBD TBD

Linear Programming $($LP$)$ Model:

Let's denote:

x$1$x$1$ as the quantity of B$1$ to be produced $($in kg$)$

x$2$x$2$ as the quantity of B$2$ to be produced $($in kg$)$

Objective Function $($Maximize Profit$)$:

Z$=6$x$1+$p$2$x$2$Z$=6$x$1+$p$2$x$2$

Constraints:

Drying Process $($M$1)$:

$30$x$1+15$x$2<=60030$x$1+15$x$2<=600($Since the factory operates for $10$ hours, $8$am$-6$pm$)$

Shelling Process $($M$2)$:

p$21$x$1+$p$22$x$2<=480$p$21$x$1+$p$22$x$2<=480($The processing time per kg for M$2$ is missing$)$

Polishing Process $($M$3)$:

p$31$x$1+$p$32$x$2<=600$p$31$x$1+$p$32$x$2<=600($The processing time per kg for M$3$ is missing$)$

Non$-$negativity:

x$1,$x$2>=0$x$1,$x$2>=0$