d cherry has a selling price of $4 per kg. The ry is 4, 6 and 2 tonne, respectively. The fer ry is 100, 100 and 50 kg, respectively. An rs each whereas an acre of peach requires
d cherry has a selling price of $4 per kg. The ry is 4, 6 and 2 tonne, respectively. The fer ry is 100, 100 and 50 kg, respectively. An rs each whereas an acre of peach requires
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Do c)
![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.
(c) Regenerate the sensitivity report given below by using Excel's Solver.
Variable Cells
Final Reduced Objective Allowable Allowable
Value Cost Coefficient Increase Decrease
Cell
Name
$B$6 Value Lemon (x1)
-920
$C$6 Value Peach (x2)
0
$D$6 Value Cherry (x3)
-820
Constraints
Final Shadow
Constraint Allowable Allowable
Increase Decrease
Cell
Name
Value
Price
R.H. Side
$B$9 Land (acre) (LHS)
8320
$B$10 Labour (hour) (LHS)
0
(d) From the above sensitivity report, answer the following questions.
(i) Interpret the reduced cost for the decision variable of cherry in terms of profit
contribution and optimal solution.
(ii) Interpret the shadow prices for the land and labour constraints, respectively.
(iii) Find the right hand side range for the labour constraint. Interpret the result about the
shadow price, optimal solution and the value of the optimal solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53d7cf85-38ef-4e29-990a-1b88e048b96f%2F9d82f1b3-df3f-49c2-8d33-a3b4a9669bc6%2Fe9td2ts_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.
(c) Regenerate the sensitivity report given below by using Excel's Solver.
Variable Cells
Final Reduced Objective Allowable Allowable
Value Cost Coefficient Increase Decrease
Cell
Name
$B$6 Value Lemon (x1)
-920
$C$6 Value Peach (x2)
0
$D$6 Value Cherry (x3)
-820
Constraints
Final Shadow
Constraint Allowable Allowable
Increase Decrease
Cell
Name
Value
Price
R.H. Side
$B$9 Land (acre) (LHS)
8320
$B$10 Labour (hour) (LHS)
0
(d) From the above sensitivity report, answer the following questions.
(i) Interpret the reduced cost for the decision variable of cherry in terms of profit
contribution and optimal solution.
(ii) Interpret the shadow prices for the land and labour constraints, respectively.
(iii) Find the right hand side range for the labour constraint. Interpret the result about the
shadow price, optimal solution and the value of the optimal solution.
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