If the revenue function is R(x) = 50x - 0.5x^2, find the number of units that ma

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Question: If the revenue function is R(x) = 50x - 0.5x^2, find the number of units that maximizes revenue. (2023)

Options:

Correct Answer: 25

Exam Year: 2023

Solution:

Max revenue occurs at x = -b/(2a) = -50/(2*-0.5) = 50.

If the revenue function is R(x) = 50x - 0.5x^2, find the number of units that maximizes revenue. (2023)

If the revenue function is R(x) = 50x - 0.5x^2, find the number of units that maximizes revenue. (2023)

Step 1: Identify the revenue function, which is R(x) = 50x - 0.5x^2.
Step 2: Recognize that this is a quadratic function in the form of R(x) = ax^2 + bx + c, where a = -0.5 and b = 50.
Step 3: To find the number of units that maximizes revenue, use the formula x = -b/(2a).
Step 4: Substitute the values of a and b into the formula: x = -50/(2 * -0.5).
Step 5: Calculate the denominator: 2 * -0.5 = -1.
Step 6: Now calculate x: x = -50 / -1 = 50.
Step 7: Conclude that the number of units that maximizes revenue is 50.

Quadratic Functions – Understanding how to find the vertex of a quadratic function to determine maximum or minimum values.
Revenue Maximization – Applying calculus or algebraic methods to find the quantity of goods that maximizes revenue.