Yogi Maharaj, Inc. is one of the leading retailers of specialty donuts with stores in most major US cities. They recently changed from a price of $$3\mathrm{.}33$ per dozen donuts, at which they sold $18,400$ dozen donuts per week to a new, higher price of $$4\mathrm{.}76$ per dozen donuts. At this new price point, Yogi has sold $15,900$ donuts. Variable costs per dozen donuts are estimated at $$0\mathrm{.}63.$

What is the optimal $($profit maximizing$)$ price for a dozen of Yogi's donuts?