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Full Name: (please PRINT clearly) Hazelnut orchards are a common sight throughout the Willamette Valley. In fact, over 99% of all hazelnuts in the United States are grown right here in the Willamette Valley. A mature hazelnut tree (12 years or older) can produce 32 pounds of nuts per year if they have plenty of space. Suppose you are starting a new hazelnut farm and have read that putting 80 trees on an acre of land will give them enough space to produce the maximum yield of 32 pounds of nuts per tree. Your goal, however, is not to make sure each tree has a maximum yield, but rather to maximize the yield of the entire orchard. So it may make sense to plant a few more trees per acre, even if doing so means each tree doesn't give you the full 32 pounds. If the average yield per tree drops 1/5 of a pound for each extra tree planted, how many trees should be planted per acre in order to maximize the amount of hazelnuts harvested? And how big is that maximum harvest per acre?

Full Name: (please PRINT clearly) Hazelnut orchards are a common sight throughout the Willamette Valley. In fact, over 99% of all hazelnuts in the United States are grown right here in the Willamette Valley. A mature hazelnut tree (12 years or older) can produce 32 pounds of nuts per year if they have plenty of space. Suppose you are starting a new hazelnut farm and have read that putting 80 trees on an acre of land will give them enough space to produce the maximum yield of 32 pounds of nuts per tree. Your goal, however, is not to make sure each tree has a maximum yield, but rather to maximize the yield of the entire orchard. So it may make sense to plant a few more trees per acre, even if doing so means each tree doesn't give you the full 32 pounds. If the average yield per tree drops 1/5 of a pound for each extra tree planted, how many trees should be planted per acre in order to maximize the amount of hazelnuts harvested? And how big is that maximum harvest per acre?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Now multiply your expressions for Tand Pto get an equation for the hazelnut harvest. Simplify your equation as much as possible. Your equation should be quadratic. H = T· P = Use the grid below to sketch a graph of your Hazelnut Harvest equation. Make sure to label your axis and clearly mark the point where the maximum occurs. Use your calculator to help you find the exact location of the maximum. Based on your work, how many trees would give the maximum harvest, and how many pounds of hazelnuts would be produced?
Transcribed Image Text:Now multiply your expressions for Tand Pto get an equation for the hazelnut harvest. Simplify your equation as much as possible. Your equation should be quadratic. H = T· P = Use the grid below to sketch a graph of your Hazelnut Harvest equation. Make sure to label your axis and clearly mark the point where the maximum occurs. Use your calculator to help you find the exact location of the maximum. Based on your work, how many trees would give the maximum harvest, and how many pounds of hazelnuts would be produced?
MTH070 Project #3: Hazelnuts Instructor: Nolan Mitchell Full Name: (please PRINT clearly) Hazelnut orchards are a common sight throughout the Willamette Valley. hazelnuts in the United States are grown right here in the Willamette Valley. In fact, over 99% of all A mature hazelnut tree (12 years or older) can produce 32 pounds of nuts per year if they have plenty of space. Suppose you are starting a new hazelnut farm and have read that putting 80 trees on an acre of land will give them enough space to produce the maximum yield of 32 pounds of nuts per tree. Your goal, however, is not to make sure each tree has a maximum yield, but rather to maximize the yield of the entire orchard. So it may make sense to plant few more trees per acre, even if doing so means each tree doesn't give you the full 32 pounds. If the average yield per tree drops 1/5 of a pound for each extra tree planted, how many trees should be planted per acre in order to maximize the amount of hazelnuts harvested? And how big is that maximum harvest per acre? Let's start by establishing a baseline. The size of the total harvest is simply the number of trees times the number of pounds each tree produces. With 80 trees per acre each producing 32 pounds of nuts, how many pounds of hazelnuts would be harvested per acre? Н — Т. Р%3 Since we intend on adding more trees, we must write equations for the number of trees T and the pounds produced Pbased on the number x of extra trees. Complete both of those equations below. Total number of trees: T = 80 + Pounds of hazelnuts per tree: P = 32 –
Transcribed Image Text:MTH070 Project #3: Hazelnuts Instructor: Nolan Mitchell Full Name: (please PRINT clearly) Hazelnut orchards are a common sight throughout the Willamette Valley. hazelnuts in the United States are grown right here in the Willamette Valley. In fact, over 99% of all A mature hazelnut tree (12 years or older) can produce 32 pounds of nuts per year if they have plenty of space. Suppose you are starting a new hazelnut farm and have read that putting 80 trees on an acre of land will give them enough space to produce the maximum yield of 32 pounds of nuts per tree. Your goal, however, is not to make sure each tree has a maximum yield, but rather to maximize the yield of the entire orchard. So it may make sense to plant few more trees per acre, even if doing so means each tree doesn't give you the full 32 pounds. If the average yield per tree drops 1/5 of a pound for each extra tree planted, how many trees should be planted per acre in order to maximize the amount of hazelnuts harvested? And how big is that maximum harvest per acre? Let's start by establishing a baseline. The size of the total harvest is simply the number of trees times the number of pounds each tree produces. With 80 trees per acre each producing 32 pounds of nuts, how many pounds of hazelnuts would be harvested per acre? Н — Т. Р%3 Since we intend on adding more trees, we must write equations for the number of trees T and the pounds produced Pbased on the number x of extra trees. Complete both of those equations below. Total number of trees: T = 80 + Pounds of hazelnuts per tree: P = 32 –
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