The Barrett Textile Mill was checked by inspectors enforcing Occupational Safety and Health Administration (OSHA) codes. The inspectors found violations in four categories: hazardous materials, fire protection, hand-powered tools, and machine guarding. In each category the mill was not in 100% compliance. Each percentage point of increase in the compliance level in each category will reduce the frequency of accidents, decrease the accident cost per worker, and constitute progress toward satisfying the OSHA compliance level. However, achieving compliance does cost the mill money. The following table shows the benefits (in accident frequency and accident cost per worker) and the costs of a percentage point increase in compliance in each category:

To achieve 100% compliance in all four categories, the mill will have to increase compliance in hazardous materials by 60 percentage points (i.e., it is now at 40% compliance), in fire protection by 28 percentage points, in hand-powered tools by 35 percentage points, and in machine guarding by 17 percentage points. However, the management of the mill faces a dilemma, in that only $52,000 is available to spend on safety. Any larger expenditure could jeopardize the financial standing of the mill. Thus, management hopes to achieve a level of accident reduction and compliance that is within the company€™s budget limitation and that will satisfy OSHA authorities enough to temporarily delay punitive action. Therefore, management has established four goals, listed here in order of importance:
(1) Do not exceed the budget constraint of $52,000.
(2) Achieve the percentage increases in compliance necessary to achieve 100% compliance in each category.
(3) Achieve total accident frequency reduction of 20 accidents/105 hours of exposure. (This goal denotes management€™s desire to minimize the frequency of accidents even if 100% compliance cannot be achieved in all categories.)
(4) Reduce the total accident cost per worker by $115.
a. Formulate a goal programming model to determine the percentage points of compliance needed in each category to satisfy the goals.
b. Solve this model by using thecomputer.

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Accident Frequency Reduction (accidents 105 hr. of exposure) Accident Cost/ Cost/Percentage Worker Reduction Point Compliance Category 1. Hazardous materials 2. Fire protection 3. Hand-powered tools 4. Machine guarding 0.18 0.11 0.17 0.21 $1.21 0.48 0.54 1.04 $135 87 58 160