Problem $1.$ You are given the following linear programming problem regarding production of two products X$1$ and X$2.$

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

Subject to:

$4x1+6x_{2}84(Timein$ department $1)$

$2x1+1x_{2}20(Timein$ Department $2)$

$4x160(Timein$ Department $3)$

Standard Form:

$4x1+6x2+S1=84($Time in department $1)$

$2x1+1x2-52=20($Time in Departm$$nt $2)$

$4$X$1,+$ S$3=60($Time in 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

YOUR ANSWERS:

Optimum solution $1$:

$x1=$

$x_2=$

$$1=$

$S2=,S3=$

$Z=$

Optimum solution $2$: $($if there is a second optimum solution$)$

$x1=,x2=,S1=,S2=S3=,Z=$

SHOW YOUR GRAPH BELOW: