Yield from an Apple Orchard Figure (shown below) is a graph of the annual yield, y(t), in bushels per year, from an orchard t years after planting. The trees take about 10 years to get established, but for the next 20 years they give a substantial yield. After about 30 years, however, age and disease start to take their toll, and the annual yield falls off y (annual yield) 500 400 300 200 100 10 20 30 40 50 60 (time in years) A. Write an expression for the average annual yield, a(M), up to M years. B. When should the orchard be cut down and replanted? Assume that we want to maximize average revenue per year, and that fruit prices remain constant, so that this is achieved by maximizing average annual yield. Use the graph of y(t) to estimate the time at which the average annual yield is a maximum.
Yield from an Apple Orchard Figure (shown below) is a graph of the annual yield, y(t), in bushels per year, from an orchard t years after planting. The trees take about 10 years to get established, but for the next 20 years they give a substantial yield. After about 30 years, however, age and disease start to take their toll, and the annual yield falls off y (annual yield) 500 400 300 200 100 10 20 30 40 50 60 (time in years) A. Write an expression for the average annual yield, a(M), up to M years. B. When should the orchard be cut down and replanted? Assume that we want to maximize average revenue per year, and that fruit prices remain constant, so that this is achieved by maximizing average annual yield. Use the graph of y(t) to estimate the time at which the average annual yield is a maximum.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Yield from an Apple Orchard Figure
(shown below) is a graph of the
annual yield, y(t), in bushels per year,
from an orchard t years after
planting.
The trees take about 10 years to get
established, but for the next 20
years they give a substantial yield.
After about 30 years, however, age
and disease start to take their toll,
and the annual yield falls off
y (annual yield)
500
400
300
200
100
10 20 30 40 50
60
(time in years)
A. Write an expression for the
average annual yield, a(M), up to
M years.
B. When should the orchard be cut
down and replanted? Assume
that we want to maximize
average revenue per year, and
that fruit prices remain constant,
so that this is achieved by
maximizing average annual yield.
Use the graph of y(t) to estimate
the time at which the average
annual yield is a maximum.
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