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154 CHAPTER 4 LINEAR PROGRAMMING APPLICATIONS

Figure 4.3 The Excel Solution for the McCormick Manufacturing Company Problem with no Workforce
Transfers Permitted

TARGET CELL (MAX)
Name Original Value Final Value
------------------ -------------- -----------
Objective function 0 73589.74359

ADJUSTABLE CELLS
Name Original Value Final Value
-------- -------------- -----------
Units P1 0 5743.589744
Units P2 0 1794.871795

CONSTRAINTS
Name Cell Value Status Slack
------ ---------- ---------- ----------
Dept. 1 5438.461538 Not Binding 1061.538462
Dept. 2 4110.25641 Not Binding 1889.74359
Dept. 3 7000 Binding 0
Dept. 4 1400 Binding 0
ADJUSTABLE CELLS
Final Reduced Objective Allowable Allowable
Name Value Cost Coefficient Increase Decrease
------- ---------- ------ ---------- ---------- --------
Units P1 5743.589744 0 10 2.857142857 5.5
Units P2 1794.871795 0 9 11 2

CONSTRAINTS
Final Shadow Constraint Allowable Allowable
Name Value Price R.H. Side Increase Decrease
------ ---------- ---------- --------- ---------- ----------
Dept. 1 5438.461538 0 6500 1E+30 1061.538462
Dept. 2 4110.25641 0 6000 1E+30 1889.74359
Dept. 3 7000 8.461538462 7000 2333.333333 3733.333333
Dept. 4 1400 10.25641026 1400 418.1818182 350

EXCEL file
McCormick
b i ¼ the labour-hours allocated to department i for i ¼ 1; 2; 3; and 4
t ij ¼ the labour-hours transferred from department i to department j

The right-hand sides are With the addition of decision variables b 1 , b 2 , b 3 and b 4 , we write the capacity
now treated as decision restrictions for the four departments as follows:
variables.

0:65P 1 þ 0:95P 2 b 1
0:45P 1 þ 0:85P 2 b 2
1:00P 1 þ 0:70P 2 b 3
0:15P 1 þ 0:30P 2 b 4

Since b 1 , b 2 , b 3 and b 4 are now decision variables, we follow the standard practice of
placing these variables on the left side of the inequalities, and the first four con-
straints of the linear programming model become:

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