Questions

Consider the following multi$-$objective Linear Program $($LP$)$:

$min{z}_1=2x_1+4x_2$

$max{z}_2=3x_1+x_2$

subject to:

$x_1+x_{2}8$

$-x_1+2x_{2}2$

$x_{1}1$

$x_{2}0$

$($a$)$ Determine graphically whether each of the following points is efficient, dominated or

infeasible $($show the graph and points$)$:

i$.(1,1\mathrm{.}5)$

ii$.(1,7)$

iii. $(2,2)$

iv$.(2,4)$

v$.(5,4)$

$($b$)$ Graphically depict the efficient frontier of this model. Show all your steps.

$($c$)$ Use pre$-$emptive optimisation to compute a solution for this model $($use $z_2$ as the first

priority objective$).$ Show all your steps and results.