A maximizing linear programming problem with variables $x$ and $Y$ and constraints $C1,C2,$ and $C3$ has been solved with the solution $x^{**}=0$ and $Y^{**}=0.$ The dual values associated with the constraints are $C1=$$$2,C2=$$$0\mathrm{.}50,$ and $C3=$$$0.$ Which statement below is false?

A$.$ One more unit of the resource in $C1$ would add $$2$ to the objective function value.

D$.$ The resources in C$1$ and in C$2,$ but not in C$3,$ are scarce.

B$.$ One more unit of the resource in C$2$ would add one more unit each of $x$ and $Y.$

E$.$ All of them are true.

C$.$ The resource in C$3$ has not been used up