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 solution to this problem $x_1=0$ and $x_2=20.$

For the solution to this problem $x_1=20$ and $x_2=0.$

For the solution to this problem $x_1=40$ and $x_2=0.$

For the solution to this problem $x_1=0$ and $x_2=40.$

None of the above