Glucose + 2 Pi + 2 ADP → 2 lactate + 2 ATP + 2 H₂O. The overall glycolysis reaction shown above occurs in eleven enzyme-catalyzed steps. If the sole consideration is to produce ATP, four of these steps could be eliminated. Altering the remaining seven steps to accommodate these deletions would still result in the same overall equation. What are the four steps which could be eliminated? Give some possible reasons why they are still included in the pathway.

The steps are 

1. hexokinase

2.phosphoglucose isomerase

3. phosphofructokinase

4.aldolase

5.triose phosphate isomerase 

6.glyceraldehyde-3-phosphate dehydrogenase

7. phosphoglycerate kinase

8. phosphoglycerate mutase

9. enolase

10. pyruvate kinase