Solve the following goal programming model graphically and then answer the multiple choice questions that follow.

minimize $P_1{d}_1^{+},P_2{d}_2^{-},P_3{d}_3^{-}$

subject to:

$4x_1+2x_2+d_1^{-}-d_1^{+}=80$

$x_1+d_2^{-}-d_2^{+}=30$

$x_2+d_3^{-}-d_3^{+}=50$

$x_j,d_i^{-},d_i^{+}0$

Which of the following is true?

For the second constraint, you would shade towards the origin.

For the third constraint, you would shade toward the origin.

For the second constraint, you would shade away from the origin.

Both a and $b.$

None of the above