The annual yield per fruit tree is fairly constant at 150...

Name: Problem 23, Chapter 3: Precalculus
Uploaded: 2020-06-10T16:32:34-08:00
Duration: 6 min 7 s
Channel: Suman Saurav Thakur
Description: The annual yield per fruit tree is fairly constant at 150 pounds per tree when the number of trees per acre is 35 or fewer. For each additional tree over 35, the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding. How many fruit trees should be planted per acre to maximize the annual yield for the acre? What is the maximum number of pounds of fruit per acre?

The annual yield per fruit tree is fairly constant at 150 pounds per tree when the number of trees per acre is 35 or fewer. For each additional tree over 35, the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding. How many fruit trees should be planted per acre to maximize the annual yield for the acre? What is the maximum number of pounds of fruit per acre?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Quadratic Function Modeling

This concept involves formulating real?world situations using quadratic functions. In optimization problems, key relationships such as yield versus quantity are expressed in the form of a quadratic equation, which then allows one to analyze and determine maximum or minimum values using mathematical techniques.

Optimization of Quadratic Functions

Optimization deals with finding the maximum or minimum values of a function. For quadratic functions, which graph as parabolas, the maximum (or minimum) value occurs at the vertex. This concept is crucial for solving problems where the goal is to maximize or minimize a certain outcome, such as total yield in an agricultural setting.

Vertex Formula

The vertex formula is a key tool in optimizing quadratic functions. It provides the x-coordinate of the vertex as -b/(2a) for a quadratic function ax² + bx + c. This concept simplifies the process of finding the optimum point, which is particularly useful when determining the level of an input (such as number of trees) that yields the highest output.

Transcript

Please give Ace some feedback