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If the revenue function is R(x) = 20x - 0.5x^2, find the quantity that maximizes
If the revenue function is R(x) = 20x - 0.5x^2, find the quantity that maximizes revenue. (2021)
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If the revenue function is R(x) = 20x - 0.5x^2, find the quantity that maximizes revenue. (2021)
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R'(x) = 20 - x = 0 gives x = 20. This maximizes revenue.
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Q: If the revenue function is R(x) = 20x - 0.5x^2, find the quantity that maximizes revenue. (2021)
Solution:
R'(x) = 20 - x = 0 gives x = 20. This maximizes revenue.
Steps: 6
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Step 1: Understand the revenue function R(x) = 20x - 0.5x^2. This function tells us how much money we make based on the quantity x sold.
Step 2: To find the quantity that maximizes revenue, we need to find the derivative of the revenue function, which is R'(x).
Step 3: Calculate the derivative R'(x). The derivative of R(x) = 20x - 0.5x^2 is R'(x) = 20 - x.
Step 4: Set the derivative equal to zero to find the critical points: 20 - x = 0.
Step 5: Solve for x. Adding x to both sides gives us 20 = x, so x = 20.
Step 6: This value of x (20) is the quantity that maximizes revenue.
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