Foreword: I ask NOT about the whole question; so I quote only the following part of the answer.
Source: p 153, Question 7c, Principles of Microeconomics, 7 Ed, 2014, by NG Mankiw
= Chapter 7, Question 6c, Principles of Microeconomics, 4 Ed, 2008, by NG Mankiw
... To take the most dramatic case, suppose the supply curve were horizontal, as shown in Figure 12. Then there is no producer surplus at all. ...
From the graph, I see that perfectly elastic supply $\iff$ a flat supply curve
$\iff$ producer surplus := Amount received by sellers $-$ Cost to sellers $\qquad = 0$.
But please help me dig deeper than the graph, which I already understand and so ask NOT about. Intuitively, why is the above true? I seek only intuition; no maths arguments or formal proofs please.