Fertilizer
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A common way of increasing agricultural yield is to spread fertilizer,
in the form of nitrogen compounds, in the fields. But fertilizer is
expensive and must be used wisely lest its cost outstrips the gain from increased
production. At agricultural research institutes
around the world experiments are conducted with
varying amounts of fertilizer to determine how efficient the
use of various amounts of fertilizer is and to advise growers
about the amount of fertilizer to use.
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An agricultural research institute
has undertaken reserach on the use of nitrogen fertilizer
in growing corn. The researchers determined that the
following quadratic function approximately describes
the dependence of the corn yield on the amount of
nitrogen fertilizer used.
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| yield in bushels per acre |
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nitrogen in kilograms
per acre |
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Advise corn growers about the amount of fertilizer to use
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Under the (unrealistic) assumption
that the corn grower has an unlimited supply of nitrogen fertilizer,
what amount would you advise to use on each acre?
What will be the yield per acre if the grower
accepts your recommendation?
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The price of nitrogen is
20 cents per kilogram. The expected price of corn this year is
$1.5 per bushel. What is the amount of nitrogen
you advise growers to use on each acre? What will be the
yield per acre?
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A sharp rise in the price of
natural gas has led to the doubling of the price of nitrogen
fertilizer to 40 cents per kilogram. The response of one
corn grower was to halve the amount of fertilizer used on each
acre, so that the total cost of fertilizer did not change.
Do you think the grower made the right decison?
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Following a drought in one of the major corn-growing regions, the price of corn has doubled and reached
$3 per bushel. How will your advice change? How will this
affect yield per acre?
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