A mini zoo is engaged in animal breeding where the animals require three different nutrients everyday. The minimum requirement for calories is 216g per day while the minimum requirement for protein and sodium is 72g and 200mg per day, respectively. Zookeeper would like to give the animals a mix of product Alpha and product Beta to provide the minimum nutritional requirement. The product cost per unit of Alpha is Rp. 40 and the product cost per unit of Beta is Rp. 80. A unit of product Alpha contains 72g of calories, 6g of protein and 40mg of sodium. While a unit of product Beta contains 12g, 24g and 20mg of calories, protein and sodium, respectively. (a) Formulate a linear programming model on deciding the mix number unit of product in order to provide the minimum nutritional requirement with the minimum cost. (b) Find the feasible region by using graphical method and list all the extreme points. (c) What is the optimal mix number unit of product in order to provide the minimum nutritional requirement with the minimum cost? State the minimum cost required. (d) If a small change occur for the product cost of Alpha; in what small range of the change could remains the current optimal? (e) On the basis of (d), compute the objective coefficient range for product Alpha.
A mini zoo is engaged in animal breeding where the animals require three different nutrients everyday. The minimum requirement for calories is 216g per day while the minimum requirement for protein and sodium is 72g and 200mg per day, respectively. Zookeeper would like to give the animals a mix of product Alpha and product Beta to provide the minimum nutritional requirement. The product cost per unit of Alpha is Rp. 40 and the product cost per unit of Beta is Rp. 80. A unit of product Alpha contains 72g of calories, 6g of protein and 40mg of sodium. While a unit of product Beta contains 12g, 24g and 20mg of calories, protein and sodium, respectively. (a) Formulate a linear programming model on deciding the mix number unit of product in order to provide the minimum nutritional requirement with the minimum cost. (b) Find the feasible region by using graphical method and list all the extreme points. (c) What is the optimal mix number unit of product in order to provide the minimum nutritional requirement with the minimum cost? State the minimum cost required. (d) If a small change occur for the product cost of Alpha; in what small range of the change could remains the current optimal? (e) On the basis of (d), compute the objective coefficient range for product Alpha.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
Do c).
Transcribed Image Text:A mini zoo is engaged in animal breeding where the animals require three different nutrients
everyday. The minimum requirement for calories is 216g per day while the minimum
requirement for protein and sodium is 72g and 200mg per day, respectively. Zookeeper would
like to give the animals a mix of product Alpha and product Beta to provide the minimum
nutritional requirement. The product cost per unit of Alpha is Rp. 40 and the product cost per
unit of Beta is Rp. 80. A unit of product Alpha contains 72g of calories, 6g of protein and 40mg
of sodium. While a unit of product Beta contains 12g, 24g and 20mg of calories, protein and
sodium, respectively.
(a) Formulate a linear programming model on deciding the mix number unit of product in order
to provide the minimum nutritional requirement with the minimum cost.
(b) Find the feasible region by using graphical method and list all the extreme points.
(c) What is the optimal mix number unit of product in order to provide the minimum nutritional
requirement with the minimum cost? State the minimum cost required.
(d) If a small change occur for the product cost of Alpha; in what small range of the change
could remains the current optimal?
(e) On the basis of (d), compute the objective coefficient range for product Alpha.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps with 1 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.