y acre he plants with maize and $3,000 for every acre he plants with sugarcane. His use of a necessary pesticide is limited by government regulations to 10 gallons for his entire 8 acres. Maize requires 2 gallons of pesticide for every acre planted and sugarcane requires just 1 gallon per acre. Given the situation James is facing, he wants to divide the land in a combination of maize and sugarcane plantations, such that he could maximise the profit he receives from his farming business while complying with the government regulations on pesticide use. One way James could achieve his goal is to try
James is a farmer who owns 8 acres of agriculture land. He can plant the land with maize and sugarcane. He can earn $5,000 for every acre he plants with maize and $3,000 for every acre he plants with sugarcane. His use of a necessary pesticide is limited by government regulations to 10 gallons for his entire 8 acres.
Maize requires 2 gallons of pesticide for every acre planted and sugarcane requires just 1 gallon per acre.
Given the situation James is facing, he wants to divide the land in a combination of maize and sugarcane plantations, such that he could maximise the profit he receives from his farming business while complying with the government regulations on pesticide use.
One way James could achieve his goal is to try the “trial and error” method, by trying different combinations of maize and sugarcane and seeing how much profit he can make from each combination.However, James’ daughter, Sara, studies linear programming and she helped her father to solve the problem using linear programming.
Question: what combination of maize and sugarcane plantation did Sara suggest to James, and what was the final profit that James achieved with that combination?
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