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158 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS
Figure 4.4 Excel Solution for the McCormick Manufacturing Company Problem
TARGET CELL (MAX)
Name Original Value Final Value
----------------- ------------- ----------
Objective function 0 84011.29944
ADJUSTABLE CELLS
Name Original Value Final Value
----- ------------- ----------
P1 0 6824.858757
P2 0 1751.412429
b1 0 6100
b2 0 4559.887006
b3 0 8050.847458
b4 0 1549.152542
t12 0 0
t13 0 400
t23 0 650.8474576
t24 0 149.1525424
t34 0 0
t41 0 0
t42 0 0
CONSTRAINTS
Name Cell Value Status Slack
--------- ----------- ---------- ----------
Dept. 1 1.81899E-12 Binding 0
Dept. 2 0 Binding 0
Dept. 3 1.81899E-12 Binding 0
Dept. 4 -2.27374E-13 Binding 0
Balance 1 6500 Binding 0
Balance 2 5359.887006 Not Binding 640.1129944
Balance 3 7000 Binding 0
Balance 4 1400 Binding 0
Transfer 1 400 Binding 0
Transfer 2 800 Binding 0
Transfer 3 0 Not Binding 100
Transfer 4 0 Not Binding 200
We define the decision variables as:
x ij ¼ litres of component i used in fuel j;
where i ¼ 1; 2; or 3 for components 1; 2; or 3;
and j ¼ r if regular or j ¼ p if premium
The six decision variables are:
x 1r ¼ litres of component 1 in regular fuel
x 2r ¼ litres of component 2 in regular fuel
x 3r ¼ litres of component 3 in regular fuel
x 1p ¼ litres of component 1 in premium fuel
x 2p ¼ litres of component 2 in premium fuel
x 3p ¼ litres of component 3 in premium fuel
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