Answered

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Your farm encompasses 900 acres, and you are planning to grow soybeans, corn, and wheat in the coming planting season. Fertilizer costs per acre are: $5 for soybeans, $2 for corn, and $1 for wheat. You estimate that each acre of soybeans will require an average of 5 hours of labor per week, while tending to corn and wheat will each require an average of 2 hours per week. Based on past yields and current market prices, you estimate a profit of $9,000 for each acre of soybeans, $6,000 for each acre of corn, and $3,000 for each acre of wheat. You can afford to spend no more than $5,400 on fertilizer, and your farm laborers can supply 5,400 hours per week. How many acres of each crop should you plant to maximize total profits

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Answer:

Using solver, the optimal solution = 900 acres of soybean resulting in $8,100,000 profit

Explanation:

you need to maximize 9000S + 6000C + 3000W

where:

S = acres of soybean

C = acres of corn

W = acres of wheat

constraints:

S + C + W ≤ 900

5S + 2C + 1W ≤ 5400

5S + 2C + 2W ≤ 5400

S, C, W ≥ 0

S, C, W are whole numbers

Using solver, the optimal solution = 900 acres of soybean resulting in $8,100,000 profit

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