Problem Scenario: The ORSA MAC Widget Company produces three different widgets for use in ORSA MAC Math Programming Exams. The three widgets have resource requirements as follows:
|
Resource Requirements
|
|
Labor
(hr/unit)
|
Materials
(lb/unit)
|
Profit
($/unit)
|
|
Widget 1
|
5
|
4
|
3
|
|
Widget 2
|
2
|
6
|
5
|
|
Widget 3
|
4
|
3
|
2
|
At the present time ORSA MAC Widgets has a normal production capacity of 240 hours of labor available daily and a daily supply of 400 pounds of material.
Management has developed the set of multiple goals, arranged in order of their importance to the firm.
- Because of labor relations difficulties, management desires to avoid underutilization of normal production capacity (i.e. no layoffs of workers).
- Management has established a satisfactory profit level of $500 per day.
- Overtime is to be minimized as much as possible.
- Management wants to minimize the purchase of additional materials because of handling and storage problems.
Requirements:
1. Develop the algebraic model for this goal programming problem.
2. Solve as a goal programming problem and recommend a daily production schedule.