Problem A-10A farmer in Wood County has 900 acres of land. She is going to plant each acre with corn, soybeans, orwheat. Each acre planted with corn yields a $2,000 profit; each with soybeans yields $2,500 profit; andeach with wheat yields $3,000 profit. She has 100 workers and 150 tons of fertilizer. The table below showsthe requirement per acre of each of the cropsCORN SOYBEANS WHEATLabor (workers)Fertilizer (tons)0.10.30.20.20.10.4Assuming a linear relationship, use the Excel Solver to determine the optimal planting mix of corn,soybeans, and wheat to maximize her profits. (Leave no cells blank - be certain to enter "0" whereverrequired. Round your answer to the nearest whole number.)Decision for cornDecision for soybeansDecision for wheatTotal profit$ResourcesUsedLabor (workers)Fertilizer (tons)Acres Planted

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Asked Dec 1, 2019
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Problem A-10
A farmer in Wood County has 900 acres of land. She is going to plant each acre with corn, soybeans, or
wheat. Each acre planted with corn yields a $2,000 profit; each with soybeans yields $2,500 profit; and
each with wheat yields $3,000 profit. She has 100 workers and 150 tons of fertilizer. The table below shows
the requirement per acre of each of the crops
CORN SOYBEANS WHEAT
Labor (workers)
Fertilizer (tons)
0.1
0.3
0.2
0.2
0.1
0.4
Assuming a linear relationship, use the Excel Solver to determine the optimal planting mix of corn,
soybeans, and wheat to maximize her profits. (Leave no cells blank - be certain to enter "0" wherever
required. Round your answer to the nearest whole number.)
Decision for corn
Decision for soybeans
Decision for wheat
Total profit
$
Resources
Used
Labor (workers)
Fertilizer (tons)
Acres Planted
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Problem A-10 A farmer in Wood County has 900 acres of land. She is going to plant each acre with corn, soybeans, or wheat. Each acre planted with corn yields a $2,000 profit; each with soybeans yields $2,500 profit; and each with wheat yields $3,000 profit. She has 100 workers and 150 tons of fertilizer. The table below shows the requirement per acre of each of the crops CORN SOYBEANS WHEAT Labor (workers) Fertilizer (tons) 0.1 0.3 0.2 0.2 0.1 0.4 Assuming a linear relationship, use the Excel Solver to determine the optimal planting mix of corn, soybeans, and wheat to maximize her profits. (Leave no cells blank - be certain to enter "0" wherever required. Round your answer to the nearest whole number.) Decision for corn Decision for soybeans Decision for wheat Total profit $ Resources Used Labor (workers) Fertilizer (tons) Acres Planted

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Expert Answer

Step 1

Determine the optimal solution:

C refers to corn, S refers to soybeans, and W refers to wheat.

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В с D 2000C+2500S+3000W 1 Maximize Z 2 C+S+W 900 Resource acre 3 0.1C+0.3S+0.2W 4 0.2C+0.1S+0.4W| Resource labor 100 Resource fertilizer 150 5 6 C 700 100 7 S 8 W 9 Total profit (Z) 1650000 10 Resource used 11 12 Resource labor 13 Resource fertilizer 14 Resource acre 100 660020 800

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Step 2

Formulae to solve the prob...

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