A farmer has 50-acre farm on which to plant pepper and tomatoes. The farmer has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping space for a maximum of 26 acres’ worth of pepper and 37 acres’ worth of tomatoes. An acre of pepper requires 10 hours of labor and 8 tons of fertilizer, whereas an acre of tomatoes requires 3hours of labor and 20 tons of fertilizer. The profit from an acre of pepper is GH¢400, and the profit from an acre of tomatoes is GH¢300. The farmer wants to know the number of acres of pepper and tomatoes to plant to maximize profit. a) Formulate a linear programming model for this problem b) Solve this model by using graphical analysis.
A farmer has 50-acre farm on which to plant pepper and tomatoes. The farmer has available 300 hours of labor per week and 800 tons of fertilizer, and he has contracted for shipping
space for a maximum of 26 acres’ worth of pepper and 37 acres’ worth of tomatoes. An acre of pepper requires 10 hours of labor and 8 tons of fertilizer, whereas an acre of tomatoes requires 3hours of labor and 20 tons of fertilizer. The profit from an acre of pepper is GH¢400, and the profit
from an acre of tomatoes is GH¢300. The farmer wants to know the number of acres of pepper and tomatoes to plant to maximize profit.
a) Formulate a linear programming model for this problem
b) Solve this model by using graphical analysis.
c) if the amount of fertilizer required for each acre of pepper were determined to be 20 tons instead of 8 tons, what would be the effect on the optimal solution?
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