Mr. Yara has 200 acres of land available to plant for three types of fruit trees (lemon, peach and cherry). Based on the market survey, lemon has a selling price of $2 per kg; peach has a selling price of $1.5 per kg and cherry has a selling price of $4 per kg. The average yield per acre for lemon, peach and cherry is 4, 6 and 2 tonne, respectively. The fertilizer requires per acre for lemon, peach and cherry is 100, 100 and 50 kg, respectively. An acre of lemon and cherry requires 10 labour hours each whereas an acre of peach requires 12 labour hours. Maximum availability of labour is 20,000 hours. The cost of fertilizer is $2 per kg and the cost of labour is $40 per hour. What is the optimal allocation of acre to the three types of fruit trees? [1 tonne = 1000kg] (a) Formulate a linear programming model to maximize the profit.
Mr. Yara has 200 acres of land available to plant for three types of fruit trees (lemon, peach and cherry). Based on the market survey, lemon has a selling price of $2 per kg; peach has a selling price of $1.5 per kg and cherry has a selling price of $4 per kg. The average yield per acre for lemon, peach and cherry is 4, 6 and 2 tonne, respectively. The fertilizer requires per acre for lemon, peach and cherry is 100, 100 and 50 kg, respectively. An acre of lemon and cherry requires 10 labour hours each whereas an acre of peach requires 12 labour hours. Maximum availability of labour is 20,000 hours. The cost of fertilizer is $2 per kg and the cost of labour is $40 per hour. What is the optimal allocation of acre to the three types of fruit trees? [1 tonne = 1000kg] (a) Formulate a linear programming model to maximize the profit.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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