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162 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

Figure 4.5 The Management Scientist Solution for the DOC Blending Problem

Objective Function Value = 9300.000

Variable Value Reduced Costs
-------------- --------------- -----------------
EXCEL file X1R 0.000 0.000
X2R 8000.000 0.000
DOC
X3R 2000.000 0.000
X1P 5000.000 0.000
X2P 2000.000 0.000
X3P 8000.000 0.000
Constraint Slack/Surplus Dual Prices
-------------- --------------- -----------------
1 0.000 0.580
2 0.000 0.480
3 0.000 0.240
4 3000.000 0.000
5 4000.000 0.000
6 0.000 0.000
7 1250.000 0.000
8 4000.000 0.000
9 3500.000 0.000
10 0.000 –0.080

Table 4.11 DOC Gasoline Blending Solution

litres of Component (percentage)
Fuel Component 1 Component 2 Component 3 Total
Regular 0 (0%) 8 000 (80%) 2 000 (20%) 10 000
1
1
1
Premium 5 000 (33 / 3 %) 2 000 (13 / 3 %) 8 000 (53 / 3 %) 15 000
NOTES AND COMMENTS

convenient way to define the decision variables in a blending problem is to use a matrix in which the rows
A correspond to the raw materials and the columns correspond to the final products. For example, in the
DOC blending problem, we could define the decision variables as follows:

Final Products
Regular Fuel Premium Fuel

Component 1 x 1r x 1p
Raw Materials Component 2 x 2r x 2p
Component 3 x 3r x 3p

This approach has two advantages: (1) it provides a systematic way to define the decision variables for any
blending problem; and (2) it provides a visual image of the decision variables in terms of how they are related to
the raw materials, products and each other.

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