SOLUTION: Suppose that the function of p= -1/4x+20 relates the selling price p of an item to the number of units x that are sold. Assume tha to is in dollars. For which value of x will the c

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Question 287215: Suppose that the function of p= -1/4x+20 relates the selling price p of an item to the number of units x that are sold. Assume tha to is in dollars. For which value of x will the corresponding revenue be a maximum? What is this maximum revenue and what is the unit price?
Answer by stanbon(75887) About Me  (Show Source):
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Suppose that the function of p= -1/4x+20 relates the selling price p of an item to the number of units x that are sold.
Assume that is in dollars.
For which value of x will the corresponding revenue be a maximum?
What is this maximum revenue and what is the unit price?
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If p is price and x is number units, then
revenue = x(price)
R(x) = (-1/4)x^2+20x
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This quadratic reaches a maximum when x = -b/2a = -20/(2(-1/4)) = -20/(-1/2)
= 40
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The revenue when x = 40 is (-1/4)40^2+20x = $400
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Cheers,
Stan H.
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