Linear Programming Word ProblemA farmer has 240 acres of land on which he can raise corn and or soybeans. Raising corn yields 120 bushels per acre, which can be sold for $2.40 per bushel, and raising soybeans yields 40 bushels per acre and sells for $6.00 per bushel. To obtain this price, the farmer must be able to store his crop in bins with a total capacity of 12,000 bushels. The farmer must limit each crop to no more than 10,800 bushels. Assuming the costs of raising corn and soybeans are the same, how much of each should the farmer plant in order to maximize his revenue? What is this maximum?How would I organize this info into a chart?What are the x and y values?What is the objective function?What are the constraints and why?How is this graphed?What is the feasable region and what are the corner points?What is the solution to this problem?Thank you for you help.PS- I have tried submitting this questions two other times. The first time I submitted it under calculus and was told to submit it under statistics, but it was rejected from statistics as well. I am submitting it under Algebra this time because the person who rejected it from statistics told me to submit it under mathametics, which there is no category for, so I figure Algebra was the next best thing.

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Asked Nov 19, 2019
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Linear Programming Word Problem

A farmer has 240 acres of land on which he can raise corn and or soybeans. Raising corn yields 120 bushels per acre, which can be sold for $2.40 per bushel, and raising soybeans yields 40 bushels per acre and sells for $6.00 per bushel. To obtain this price, the farmer must be able to store his crop in bins with a total capacity of 12,000 bushels. The farmer must limit each crop to no more than 10,800 bushels. Assuming the costs of raising corn and soybeans are the same, how much of each should the farmer plant in order to maximize his revenue? What is this maximum?

How would I organize this info into a chart?
What are the x and y values?
What is the objective function?
What are the constraints and why?
How is this graphed?
What is the feasable region and what are the corner points?
What is the solution to this problem?

Thank you for you help.

PS- I have tried submitting this questions two other times. The first time I submitted it under calculus and was told to submit it under statistics, but it was rejected from statistics as well. I am submitting it under Algebra this time because the person who rejected it from statistics told me to submit it under mathametics, which there is no category for, so I figure Algebra was the next best thing.

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Expert Answer

Step 1

As per the question, the farmer stores the crop in bin.

Therefore, let x be the number of corn bushels stored in the bin and y be the number of soybean bushels stored in the bin.

Now, the capacity of bushels is 12000 and the limit of each crop is no more than 10,800 bushels. From this statement, deduce the constrains.

Also find the corner points by solving the equations obtained by constraints.

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-(1) x y12000 rs10800 ys10800 x y 12000 10800y 12000 x. y)= (10800,1200) y1200 x y 12000 x10800 12000 x 1200 x, y) (1200, 10800)

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Step 2

Now, corn is sold at a price of $2.40 per bushels and soybean is sold at a price of $6.00 per bushels.

Therefore, the objective function Z = 2.40x + 6.00y.

To maximize the revenue, calculate maximum value of Z at x and y.

Step 3

Now plot the graph using the constraints and mark the corner points.

Then feasible region is the region made by the c...

help_outline

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-15000 (0, 10800) 10000 (1200, 10800) y axis 5000 (10800, 1 200) (10800, 0) 00 10000 5000 (0,0) х ахis -5000

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