A production manager is faced with the problem of job allocation between his two production teams. The production rate of the team X is 8 units per hour, while the production rate of team Y is 5 units per hour. The normal working hours for both teams are 40 hours per week. The production manager has prioritized the following goals for the coming week.

P1: Avoid underachievement of the desired production level of 550 units.

P2: Any overtime operation of team X beyond 5 hours should be avoided.

P3: The sum of the overtime for both teams should be minimized. (Assign differential weights according to the relative cost of an overtime hour - Assume that the operating costs of the two teams are identical.)

P4: Any underutilization of regular working hours should be avoided; again, assign differential weights according to the relative productivity of the two teams.

Formulate this problem as a goal programming model.

AppendixLO1