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zedanabdul198
02.08.2019 •
Mathematics
Farmer planting corn and soybeans: a farmer has a 320 acre farm on which she plants two crops: corn and soybeans. for each acre of corn planted, her expenses are $50 and for each acre of soybeans planted, her expenses are $100. each acre of corn requires 100 bushels of storage and yields a profit of $60; each acre of soybeans requires 40 bushels of storage and yields a profit of $90. if the total amount of storage space available is 19,200 bushels and the farmer has only $20,000 on hand, how many acres of each crop should she plant in order to maximize her profit? what will her profit be if she follows this strategy?
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Ответ:
Let x represents acres of corn to be planted.
Let y represents acres of soybeans to be planted.
A farmer has a 320 acre farm on which she plants two crops. We get;
Other equations as per scenario becomes:
We have to find the profit. So let the profit be p. We can give this by:
When we graph these functions, we get the following.
(0,200) putting these in
we get profit as $1800
(140,130) , we get $20,100
(192,0) we get $11520
In the graph, we have points (240,180) but this is not possible as
so, we have (140,130) to get the maximum profit.
Ответ:
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