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A farmer can plant up to 8 acres of land with grapes and tomatoes. He can earn $5,000 for every acre he plants with grapes and $3,000 for every acre he plants with tomatoes. His use of a required pesticide is limited by federal regulations to 10 gallons for his entire 8 acres. Grapes require 2 gallons of pesticide for every acre planted while tomatoes require just 1 gallon per acre. How many acres of grapes and tomatoes should be planted to achieve max profit? What is the max profit he can make?
1 Answer
- 5 years agoFavorite Answer
Let g = the number of acres of grapes. Then 8 - g is the number of tomatoes.
Let the profit in thousands of dollars = P(g).
Then P(g) = 5g + 3(8 - g) = 2g + 24
Also, 2g + (8 - g) ≤ 10
g ≤ 2.
The maximum profit occurs when g = 2, i.e. there are 2 acres of grapes and 6 acres of tomatoes. The maximum profit = P(2) = $28,000.