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:

$4$

x

$1$

$+$

$2$

x

$2$

$+$

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

$+$

$>=$

$0$