The annual Great Sofa Round$-$up is a collaborative event between Colorado State University and the City of Fort Collins aims to help students and neighbors get rid of unwanted furniture, while giving people in need access to inexpensive sofas. Suppose on the day of the Round$-$up$,$ your friends take their couches to the main parking lot on campus where the Round$-$up is held. Raj will not sell his couch for less than $$30,$ Emily will not sell her couch for less than $$50,$ Nara will not sell her couch for less than $$20,$ Sergio just wants to get rid of his couch and he is willing to give it away for free. At the Round$-$up$,$ potential buyers think that all the couches available are basically the same and they are willing to buy a couch for $$50.$ What is the value of the market producer surplus?

$$120$

$$100$

$$50$

$$200$