Answer:
q = 25
revenue = 1250
Explanation:
Given demand function p = 100 -2q, you want the maximum revenue and the quantity that produces it.
Revenue
Revenue is the product of quantity and price:
R = pq = (100 -2q)q = 2(50 -q)q
The revenue function describes a downward-opening parabola with zeros at q=0 and q=50. Revenue will be maximized by a quantity that is the average of these values:
q = (0 +50)/2 = 25
The revenue-maximizing quantity is 25.
Total revenue at that quantity is ... R = 2(50 -25)(25) = 2·25² = 1250.
The maximum revenue is 1250.
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