Solution 2.15 - Chemometrics: Data Analysis for the Laboratory and Chemical Plant

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  • Published: Jan 1, 2000
  • Channels: Chemometrics & Informatics

1. The equation is


 
2. The design matrix is as follows.

The coefficients are as follows.

b1

b2

b3

b4

b12

b13

b14

b23

b24

b34

b123

b124

b134

b234

6.86

6.5

7.29

5.88

2.52

-0.54

4.04

0.42

3.76

2.9

11.07

-8.37

-2.1

0.99

              

3. The raw numbers when A+B+C=1 are presented below. The bottom left corner number represents 100% A, the top left hand corner represents 100% C and the top right hand corner represents 100% B. To check this, the coefficient b1 should represent pure A (=6.86). 



           
The contour plot where A+B+C=1 is presented below.

When D is absent the optimal blend is a ternary mixture of the remaining three components.


4. The three contour plots are presented below. When C is absent the best blend is a binary mixture of A and D, although there is quite a restricted region. When A is absent, the best blend is a mixture of C and D. In the absence of B a mixture of either C and D or A and D would provide the best blend. In the presence of D the best blend is always a binary mixture containing D

5.  There is no guarantee that all the cultivars will be available throughout the year. Moreover, the cost of each cultivar may vary according to supply and demand or even seasonal factors. Therefore different solutions might be necessary according to other factors, including expense. Often in these cases several factors might be modelled using a mixture design and explored graphically. Note that, according to availability of raw material quite different optimal solutions are obtained.

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