We study the situation of an investor-producer who can trade on a financial market in continuous time and can transform some assets into others by means of a discrete time production system, in order to price and hedge derivatives on produced goods. This general framework covers the interesting case of an electricity producer who wants to hedge a financial position and can trade commodities which are also inputs for his system. This extends the framework of (Bouchard and Nguyen, 2011) to continuous time for concave and bounded production functions. We introduce the flexible concept of conditional sure profit along the idea of the no sure profit condition of (Rasonyi, 2009) and show that it allows one to provide a closedness property for the set of super-hedgeable claims in a very general setting. Using standard separation arguments, we then deduce a dual characterization of the latter.