Mr. Yara has 200 acres of land available to plant for three types of fruit trees (lemon, peach a cherry). Based on the market survey, lemon has a selling price of $2 per kg; peach has a selli price of $1.5 per kg and cherry has a selling price of $4 per kg. The average yield per acre lemon, peach and cherry is 4, 6 and 2 tonne, respectively. The fertilizer requires per acre lemon, peach and cherry is 100, 100 and 50 kg, respectively. An acre of lemon and cher requires 10 labour hours each whereas an acre of peach requires 12 labour hours. Maximu availability of labour is 20,000 hours. The cost of fertilizer is $2 per kg and the cost of labour $40 per hour. What is the optimal allocation of acre to the three types of fruit trees? [1 tonne = 1000k (a) Formulate a linear programming model to maximize the profit. (b) Find the optimal solution by using simplex algorithm.
Mr. Yara has 200 acres of land available to plant for three types of fruit trees (lemon, peach a cherry). Based on the market survey, lemon has a selling price of $2 per kg; peach has a selli price of $1.5 per kg and cherry has a selling price of $4 per kg. The average yield per acre lemon, peach and cherry is 4, 6 and 2 tonne, respectively. The fertilizer requires per acre lemon, peach and cherry is 100, 100 and 50 kg, respectively. An acre of lemon and cher requires 10 labour hours each whereas an acre of peach requires 12 labour hours. Maximu availability of labour is 20,000 hours. The cost of fertilizer is $2 per kg and the cost of labour $40 per hour. What is the optimal allocation of acre to the three types of fruit trees? [1 tonne = 1000k (a) Formulate a linear programming model to maximize the profit. (b) Find the optimal solution by using simplex algorithm.
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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Do b)
![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.
(b) Find the optimal solution by using simplex algorithm.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53d7cf85-38ef-4e29-990a-1b88e048b96f%2Fc445403f-51fc-40dd-9955-f159987ff9df%2Ftgnmcx4_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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.
(b) Find the optimal solution by using simplex algorithm.
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