Statistics Solutions

[Steps Shown] The price p and the quantity x sold of a certain product obey the demand equation p=-1/2 x+50, for 0 ≤q x ≤q 100. Express the revenue

Question: The price \(p\) and the quantity \(x\) sold of a certain product obey the demand equation \(p=-\frac{1}{2} x+50\), for \(0 \leq x \leq 100\).

  1. Express the revenue \(R\) as a function of \(x\).
  2. What is the revenue if 100 units are sold?
  3. Using the graph of the revenue function, what quantity $x$ maximizes revenue?
  4. What is the maximum revenue?
  5. What price should the company charge to maximize revenue?

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