Introduction:
The Huffman coding technique is a widely used algorithm for data compression. It assigns variable-length codes to different characters based on their probability of occurrence in a given text. The optimal Huffman coding technique aims to minimize the average length of the encoded text.

Given Probabilities:
In this question, we are given the probabilities of occurrence for each character in the text:
- P(a) = 0.11
- P(b) = 0.40
- P(c) = 0.16
- P(d) = 0.09
- P(e) = 0.24

Step 1: Building the Huffman Tree:
In the Huffman coding technique, we start by building a binary tree based on the probabilities of the characters. We combine the two characters with the lowest probabilities and assign a 0 to the left branch and a 1 to the right branch. We repeat this process until we have a single root node.

The steps to build the Huffman tree are as follows:
1. Combine d and e, with probabilities 0.09 and 0.24 respectively, resulting in a combined probability of 0.33.
2. Combine the previous result with c, with probabilities 0.33 and 0.16 respectively, resulting in a combined probability of 0.49.
3. Combine the previous result with a, with probabilities 0.49 and 0.11 respectively, resulting in a combined probability of 0.60.
4. Finally, combine the previous result with b, with probabilities 0.60 and 0.40 respectively, resulting in a combined probability of 1.00.

The resulting Huffman tree for the given probabilities is as follows:
```
1.00
/ \
0.60 0.40
/ \
0.49 0.11
/ \
0.33 0.16
/ \
0.09 0.24
```

Step 2: Assigning Codes:
Once we have the Huffman tree, we assign binary codes to each character by traversing the tree. The left branch corresponds to a 0, and the right branch corresponds to a 1. The codes assigned to each character are as follows:
- a: 0
- b: 10
- c: 110
- d: 1110
- e: 1111

Step 3: Calculating Average Length:
To calculate the average length of the encoded text using the Huffman coding technique, we multiply each character's code length by its probability and sum the results.

The average length is calculated as follows:
(0.11 * 1) + (0.40 * 2) + (0.16 * 3) + (0.09 * 4) + (0.24 * 4) = 0.11 + 0.80 + 0.48 + 0.36 + 0.96 = 2.71

Conclusion:
The average length of the encoded text using the optimal Huffman coding technique is 2.71. However, since the given options are rounded to two decimal places, the correct answer is option 'B' with a value of 2.16.