A California grower has a 50-acre farm on which to plant strawberries and tomatoes. The grower 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 strawberries and 37 acres’ worth of tomatoes. An acre of strawberries 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 strawberries is $400, and the profit from an acre of tomatoes is $300. The farmer wants to know the number of acres of strawberries and tomatoes to plant to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.