Suppose That Choice Sets Are Convex but We Tastes May

Suppose that choice sets are convex but we tastes may or may not be convex.(Assume all our other usual assumptions about tastes hold.)The first order conditions of the constrained utility maximization problem are then
a.
necessary conditions for a true optimum.
b.
sufficient conditions for a true optimum.
c.
necessary and sufficient conditions for a true optimum.
d.
none of the above.