Producer A and Producer B are located $200$ miles apart. Producer A has a production cost of $$120$ per unit and a transportation cost of $$1\mathrm{.}5$ per unit per mile. Producer B has a production cost of $$100$ per unit and a transportation cost of $$2\mathrm{.}5$ per unit per mile. Find the market area for Producer B from its plant $($How far Producer B can move its products towards Producer A and still have a lower landed cost?$)$