The marginal price $\frac{dp}{dx}$ at $x$ units of demand per week is proportional to the price $p.$ There is no weekly demand at a price of $$150$ per unit $p(0)=150,$ and there is a weekly demand of $6$ units at the price of $$112\mathrm{.}36$ per unit $p(6)=112\mathrm{.}36.$

Use the given information to answer the questions.