Part $1-$ Graphical Solution

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

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

Subject to:

$4x_1+6x_{2}84(Timein$ department $1)$

$2x_1+1x_{2}20(Timein$ Department $2)$

$4x160(Timein$ Department $3)$

Standard form:

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

$2x1+1x2-S2=20($Time in Department $2)$

$4x1,+S3=60($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 XI$,$ X$2$ the three slacks S$1,$ S$2,$ S$3,$

YOUR ANISWERS:

Optimum solution $1$:

$x1=,x_2=,S1=,s2=,s3=,Z=$

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

$x1=,x_2=,S1=,S2=,S3=,Z=$

SHOW YOUR GRAPH BELOW: