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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
Expert Answer
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
