A farmer has a 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 3 hours 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 farmer has a 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 3 hours 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) i. Transform the model into a standard form
ii. Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points.
iii. Using the computer, determine the shadow prices for the resources and explain their meaning (show the sensitivity report).
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