A company makes 2 products A and B from 2 resources, labor and material. The pro

Question

A company makes 2 products A and B from 2 resources, labor and material. The products have the following resource requirements and produce the accompanying profits. The available quantity of resources is also shown in the table.

Product

A

B

Available resources

Labor (hr/unit)

3

2

150

Material (ounces/unit)

1

2

200

Profit($/unit)

7

6

Management has developed the following set of goals

Goal 1: Produce at least 40 units of product A.

Goal 2: Achieve a satisfactory profit level of $400.

Goal 3: Consume less than 150 hours of labor

Formulate a goal programming model of this problem.

Product

A

B

Available resources

Labor (hr/unit)

3

2

150

Material (ounces/unit)

1

2

200

Profit($/unit)

7

6

Explanation / Answer

Let X1 = Number of Product A

        X2 = Number of Product B

Goal programming model is to be formulated

Positive & negative deviational variables are (d+) and (d-)

Here (d+) denotes quantity by which a specific level goal is surpassed & (d-) denotes quantity by which a specific goal level is underperformed or underachieved

Goal programming model is as follows

X1+d1- - d1+ =40

7X1+6X2+ d2- - d2+ =400

3X1+2X2+ d3- - d3+ =150

XI, di- , di+        0 for all i

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