How to Solve all by hand $($no excel$)?$ Kalyan Singhal Corp. makes three products, and it has three machines available as resources as given in the following LP problem:

$[$ Maximize contribution $=5$ X$\_1+4$ X$\_2+3$ X$\_3$ ; $1$ X$\_1+7$ X$\_2+4$ X$\_3<=90($C$\_1.$ : hours on machine $1)$; $2$ X$\_1+1$ X$\_2+7$ X$\_3<=96($C$\_2.$ : hours on machine $2)$; $8$ X$\_1+4$ X$\_2+1$ X$\_3<=90($C$\_3.$ : hours on machine $3)$; X$\_1,$ X$\_2,$ X$\_3>=0]$