Chapter 4.16, Problem 8P

Explanation of Solution

Formulation of pre-emptive goal programming model:

Take the following variables to solve the problem,

${\text{x}}_{\text{1}}$= Number of in state students

${\text{x}}_2$= Number of out of state students

${\text{x}}_3$= Number of nerds

${\text{x}}_4$= Number of non-nerds

${\text{d}}_{\text{1}}{}^{\text{-}}$= Underachievement in the number of student in entering class

${\text{d}}_{\text{1}}{}^{\text{+}}$= Overachievement in the number of student in entering class

${\text{d}}_{\text{2}}{}^{\text{-}}$= Underachievement in the average SAT score of entering class

${\text{d}}_{\text{2}}{}^{\text{+}}$= Overachievement in the average SAT score of entering class

${\text{d}}_{\text{3}}{}^{\text{-}}$= Underachievement in the number of out of state students in entering class

${\text{d}}_{\text{3}}{}^{\text{+}}$= Overachievement in the number of out of state students in entering class

${\text{d}}_4{}^{\text{-}}$= Underachievement in the number of non-nerds in entering class

${\text{d}}_4{}^{\text{+}}$= Overachievement in the number of non-nerds in entering class

The pre-emptive goal programming can be formulated as given below,

Minimize, $z=P_1{\text{d}}_{\text{1}}{}^{\text{-}}+P_2{\text{d}}_2{}^{\text{-}}+P_3{\text{d}}_3{}^{\text{-}}+P_4{\text{d}}_4{}^{\text{-}}$

Subject to,