[Recall the Bishop-Phelps Theorem][1].

> **Bishop-Phelps Theorem:** Let $B\subseteq E$ be a bounded, closed, convex subset of a real Banach space $E.$
Then the set 
$$\{e^*\in E^*: e^* \text{ attains its supremum on } B \}$$
is norm-dense in the dual $E^*.$

Does the theorem hold for extreme points? 
More precisely, 

> *Question:* Let $B\subseteq E$ be a bounded, closed and convex subset of a real Banach space $E.$
Is it true that the set 
$$\{e^*\in\text{ext} \left( B_{E^*} \right): e^*\text{ attains its supremum on }B\}$$
norm-dense in $\text{ext}\left( B_{E^*} \right)?$ 

If the there is an affirmative answer to my question, may I have reference? 

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*Notation:* We say that $e^*$ is an extreme point of $B_{E^*}$ if it cannot be expressed as midpoint of two elements from $B_{E^*}.$
Denote $\text{ext}\left( B_{E^*}\right)$ to be the set of all extreme points of $B_{E^*}.$

  [1]: https://en.wikipedia.org/wiki/Bishop%E2%80%93Phelps_theorem