\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The weekly revenue, \(R\), from selling a product at a price of \(p\) dollars per unit is given by the function \(R(p) = -4p^2 + 200p\).
  1. Show that the company earns no revenue if the price is \(\dollar\)50.
  2. Find the price that maximizes the weekly revenue and the value of this maximum revenue.

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