If the revenue function is R(x) = 100x - 2x^2, find the number of units that max
Practice Questions
Q1
If the revenue function is R(x) = 100x - 2x^2, find the number of units that maximizes revenue. (2021)
25
50
75
100
Questions & Step-by-Step Solutions
If the revenue function is R(x) = 100x - 2x^2, find the number of units that maximizes revenue. (2021)
Step 1: Identify the revenue function, which is R(x) = 100x - 2x^2.
Step 2: Recognize that this is a quadratic function in the form of R(x) = ax^2 + bx + c, where a = -2 and b = 100.
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 = -100/(2 * -2).
Step 5: Calculate the denominator: 2 * -2 = -4.
Step 6: Now calculate x: x = -100 / -4 = 25.
Step 7: Conclude that the number of units that maximizes revenue is 25.
Quadratic Functions – Understanding the properties of quadratic functions, particularly how to find the vertex which represents the maximum or minimum point.
Revenue Maximization – Applying calculus or algebraic methods to determine the quantity of goods that maximizes revenue.
Vertex Formula – Using the vertex formula x = -b/(2a) to find the maximum point of a quadratic function.
