# (Solved): Your farm encompasses 1000 acres, and you are planning to grow soybeans, corn

Your farm encompasses 1000 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 \$3,000 for each acre of soybeans, \$2,000 for each acre of corn, and \$1,000 for each acre of wheat. You can afford to spend no more than \$6,000 on fertilizer, and your farm laborers can supply 6,000 hours per week. How many acres of each crop should you plant to maximize total profits?

soybeans __________ acre(s)

corn ___________ acre(s)

wheat _____________ acre(s)

In this event, will you be using all the available labor?

Yes OR No

Decision variables:

Let S = No of acres of soybeans to be planted

C = No of acres of corn to be planted

W = No of acres of wheat to be planted

The objective function is maximize the profits

Z = max 3000S + 2000C +1000W

Constraints:

S+C+W <=1000

5S + 2C + 1W <= 6000

5S+2C + 2W <= 6000

S, C, W>=0

Soybeans = 1000 acres

Corn = 0 acres

Wheat = 0 acres

No we are not using all the available labor

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