Consider the Bi$-$criteria LP $($BCLP$)$ problem.

$Max{z}_1=-x_1+x_2$

$Max{z}_2=x_1$

Subject to:

$-x_1+x_{2}2$

$x_{1}7$

$x_1+x_{2}8$

$x_1,x_{2}0$

$($a$)$ Show graphically the decision space and the objective space.

$($b$)$ Identify the set of efficient solutions in both the decision space and the objective space.

$($c$)$ What is the ideal solution? Using the ideal solution, determine the best lower and upper bounds for $z_1$ and $z_2.$