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?

In the solution to this problem, all three goals are satisfied.

In the solution to this problem, goal $1$ and $2$ are satisfied.

In the solution to this problem, $d_2$ is equal to $0.$

In the solution to this problem, $d_3^{+}$is equal to $50.$

None of the above