# One of management’s goals in a goal programming problem is expressed algebraically

One of management’s goals in a goal programming problem is expressed algebraically as 3x1 + 4x2 + 2x3 = 60, where 60 is the specific numeric goal and the left-hand side gives the level achieved toward meeting this goal.

(a) Letting y + be the amount by which the level achieved exceeds this goal (if any) and y the amount under the goal (if any), show how this goal would be expressed as an equality constraint when reformulating the problem as a linear programming model.

(b) If each unit over the goal is considered twice as serious as each unit under the goal, what is the relationship between the coefficients of y+ and y in the objective function being minimized in this linear programming model.