Your farm encompasses 500 acres, and you are planning to grow soybeans, corn, and wheat in...

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Your farm encompasses 500 acres, and you are planning to growsoybeans, corn, and wheat in the coming planting season. Fertilizercosts per acre are: $5 for soybeans, $2 for corn, and $1 for wheat.You estimate that each acre of soybeans will require an average of5 hours of labor per week, while tending to corn and wheat willeach require an average of 2 hours per week. Based on past yieldsand current market prices, you estimate a profit of $10,500 foreach acre of soybeans, $7,000 for each acre of corn, and $3,500 foreach acre of wheat. You can afford to spend no more than $3,000 onfertilizer, and your farm laborers can supply 3,000 hours per week.How many acres of each crop should you plant to maximize totalprofits?
soybeans     acre(s)
corn     acre(s)
wheat     acre(s)

In this event, will you be using all the available labor?
Yes No

Answer & Explanation Solved by verified expert

4.4 Ratings (943 Votes)

Let x acres of soybeans y acres of corn z acres of wheatshould be planted to maximize total profitThen by the given conditions we haveMaximize W 10500x7000y3500zSubject to See Answer

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