Question: 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:
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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.
1) Because of labor relations difficulties, management desires to avoid underutilization of normal production capacity (i.e. no layoffs of workers).
2) Management has established a satisfactory profit level of $500 per day.
3) Overtime is to be minimized as much as possible.
4) Management wants to minimize the purchase of additional materials because of handling and storage problems.
Requirements: a) Develop the algebraic model for this goal programming problem.
b) Solve as a goal programming problem and recommend a daily production schedule.