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112 CHAPTER 3 LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION

Table 3.1 Nutritional Value and Cost Data for the KCC Problem
Feed Component Standard Enriched Additive
Ingredient A 0.8 0.2 0.0
Ingredient B 1.0 1.5 3.0
Ingredient C 0.1 0.6 2.0
Cost per kilo 25 50 300
(Kenyan shillings)

S = number of kilos of the standard product
E ¼ number of kilos of the enriched product
A ¼ number of kilos of the vitamin and mineral feed additive

Using the data in Table 3.1, the objective function for minimizing the total cost
associated with the daily feed can be written as follows:
min 25S þ 50E þ 300A
For a minimum daily requirement for ingredient A of three units, we obtain the
constraint:
0:8S þ 0:2E 3
The constraint for ingredient B is:
1:0S þ 1:5E þ 3:0A 6
and the constraint for ingredient C is:
0:1S þ 0:6E þ 2:0A 4
Finally, the constraint that restricts the mix to at most six kilos is:
S þ E þ A 6

Combining all the constraints with the nonnegativity requirements enables us to
write the complete linear programming model for the problem as follows:
Min 25S þ 50E þ 300A
s:t
0:8S þ 0:2E 3 Ingredient A
1:0S þ 1:5E þ 3:0A 6 Ingredient B
0:1S þ 0:6E þ 2:0A 4 Ingredient C
S þ E þ A 6 Weight
S; E; A 0

Computer Solution and Interpretation for the KCC Problem
The output obtained using The Management Scientist to solve the KCC problem is
shown in Figure 3.13. After rounding, we see that the optimal solution calls for a
daily diet consisting of 3.51 kilos of the standard product, 0.95 kilos of the enriched
product and 1.54 kilos of the vitamin and mineral feed additive. Thus, with feed
component costs of 25 sh., 50 sh. and 300 sh., the total cost of the optimal diet is:
3:51 kilos @ 25 sh per kilo ¼ 85 sh
0:95 kilos @ 50 sh per kilo ¼ 47 sh
1:54 kilos @ 300 sh per kilo ¼ 462 sh
Total cost ¼ 597 sh

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