Problem $1.$ You are given the following linear programming problem regarding production of two products $x1$ and $x2.$

Maximize $Z=$$$46x1+$$$69x2$

Subject to:

$4x1+6x284(Timein$ department $1)$

$2x1+1x220($ Time $in$ Department $2)$

$4x1,60(Timein$ Department $3)$

Using graphical procedure, solve the problem. $($Graph the constraints and identify the region of feasible solutions$).$ What are the values of $x1,x2$ the three slacks $S1,S2,S3,$ and the value of the objective function

$($Z$)$ at optimum? If there are multiple optimum solutions, please give two of the ontimum solutions.