WILL GIVE BRAINLIEST! Please help
Waterbrook Farm Includes 240 acres of cropland. The farm owner wishes to plant this
acreage in both corn and soybeans. The profit per acre in com production is $325 and
In soybeans is $180. A total of 320 hours of labor is available. Each acre of com
requires 2 hours of tabor, whereas each acre of soybeans requires 1 hour of labor.
Lot x = the number of acres planted with corn.
Let y = the number of acres planted with soybeans.
1) What would the farm's profits be if they planted only corn?
2) What would the farm's profits be if they planted only soybeans?
3) Find the equation for the Waterbrook Farm's profit (P = ),
4) Make a system of inequalities based off the constraints of the Farm.
5) In DESMOS. graph the system of inequalities
6) How should the land be divided between the corn and soybeans in order to yield
the mamum profit?
7) What is the maximum profit of planting both com and soybeans for the Farm?
Answers
Answer:
1) $52,000
2) $43,200
3) P = 325 × x + 180 × y
4) x + y ≤ 240
2·x + y ≤ 320
325 × x + 180 × y ≤ 52,000
5) Please find a similar graph created with MS Excel
6) Corn will have 80 acres
Soybean will have 160 acres
7) $54,800
Step-by-step explanation:
The acres of cropland at the Waterbrook Farm, A = 240 acres
The profit per acre in corn production, p₁ = $325
The profit per acre in soybean production, p₂ = $180
The hours of labor required by each acre of corn = 2 hours
The hours of labor required by each acre of soybeans = 1 hours
The number of acres planted with corn = x
The number of acres planted with soybeans = y
1) The farm's profit, 'P', if they planted only corn is P = p₁ × A
∴ P = $325/acre × 320 hours/(2 hours/acre) = $52,000
The farm's profit if they planted only corn, P = $52,000
2) The farm's profit, 'P', if they planted only corn is P = p₂ × A
The required labor for cultivating the 240 acres at 1 hour/acre = 240 hours of labor
Therefore, the labor is sufficient for the entire farmland, we get;
The profit, P = $180/acre × 240 acres = $43,200
∴ The farm's profit if they planted only soybeans, P = $43,200
3) The equation for the Waterbrook Farm's profit, 'P' can be found, depending on the area of the farm used for the corn and the soybeans as follows;
P = 325 × x + 180 × y
4) The system of inequalities includes;
x + y ≤ 240
2·x + y ≤ 320
325 × x + 180 × y ≤ 52,000
5) Using DESMOS, we have;
The graph of the systems of inequalities is plotted and a graph similar to the attached graph created with MS Excel is found
6) The maximum profit point found using DESMOS is (80, 160)
Therefore, for maximum profit, 80 acres should be used for corn while 160 acres should be used for soybeans
7) The maximum profit of planting both corn and soybeans is found from the profit obtained from the land divided between corn and soybeans in order to yield maximum profit as follows;
P = 325 × 80 + 180 × 160 = 54,800
The maximum profit of planting both corn and soybeans, P = $54,800.
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Step-by-step explanation:
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<
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Answer:
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Answer:
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х
?
Answers
Answer:
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Answers
Answer:
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Answer:
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Step-by-step explanation:
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