Homework Help is Here – Start Your Trial Now!
Business
Operations Management
Slim-Down Manufacturing makes a line of nutritionally complete, weight-reduction beverages. One of their products is a strawberry shake which is designed to be a complete meal. The strawberry shake consists of several ingredients. Some information about each of these ingredients is given below. Calories Total Vitamin Calories (per tbsp) 50 100 0 120 80 Ingredient Strawberry flavoring Cream Vitamin supplement Artificial sweetener Thickening agent from fat (per tbsp) 1 75 0 0 30 Content (mg/tbsp) 20 0 50 0 2 Thickeners (mg/tbsp) 3 8 1 2 25 Cost (c/tbsp) 10 8 25 15 6 The nutritional requirements are as follows. The beverage must total between 380 and 420 calories (inclusive). No more than 20% of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin content. For taste reasons, there must be at least two tablespoons (tbsp) of strawberry flavoring for each tbsp of artificial sweetener. Finally, to maintain proper thickness, there must be exactly 15 mg of thickeners in the beverage. Management would like to select the quantity of each ingredient for the beverage which would minimize cost while meeting the above requirements. Formulate a linear programming model for this problem.

Slim-Down Manufacturing makes a line of nutritionally complete, weight-reduction beverages. One of their products is a strawberry shake which is designed to be a complete meal. The strawberry shake consists of several ingredients. Some information about each of these ingredients is given below. Calories Total Vitamin Calories (per tbsp) 50 100 0 120 80 Ingredient Strawberry flavoring Cream Vitamin supplement Artificial sweetener Thickening agent from fat (per tbsp) 1 75 0 0 30 Content (mg/tbsp) 20 0 50 0 2 Thickeners (mg/tbsp) 3 8 1 2 25 Cost (c/tbsp) 10 8 25 15 6 The nutritional requirements are as follows. The beverage must total between 380 and 420 calories (inclusive). No more than 20% of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin content. For taste reasons, there must be at least two tablespoons (tbsp) of strawberry flavoring for each tbsp of artificial sweetener. Finally, to maintain proper thickness, there must be exactly 15 mg of thickeners in the beverage. Management would like to select the quantity of each ingredient for the beverage which would minimize cost while meeting the above requirements. Formulate a linear programming model for this problem.

Practical Management Science
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...
See similar textbooks
icon
Related questions
Question
**Slim-Down Manufacturing: Strawberry Shake Nutritional Overview** Slim-Down Manufacturing produces a range of nutritionally complete, weight-reduction beverages. Among these is a strawberry shake designed as a complete meal. Below is detailed information on the ingredients used in this shake. | Ingredient | Calories from fat (per tbsp) | Total Calories (per tbsp) | Vitamin Content (mg/tbsp) | Thickeners (mg/tbsp) | Cost (¢/tbsp) | |------------------------|-----------------------------|--------------------------|--------------------------|---------------------|--------------| | Strawberry flavoring | 1 | 50 | 20 | 3 | 10 | | Cream | 75 | 100 | 0 | 8 | 8 | | Vitamin supplement | 0 | 0 | 50 | 1 | 25 | | Artificial sweetener | 0 | 120 | 0 | 2 | 15 | | Thickening agent | 30 | 80 | 2 | 25 | 6 | **Nutritional Requirements:** 1. **Caloric Needs:** - Total calories for the beverage must be between 380 and 420 calories (inclusive). - No more than 20% of the total calories should derive from fat. 2. **Vitamin Content:** - The shake must contain at least 50 milligrams of vitamins. 3. **Flavor and Texture:** - For taste, there must be a minimum of two tablespoons of strawberry flavoring for each tablespoon of artificial sweetener. - To maintain proper thickness, the shake needs exactly 15 milligrams of thickeners. **Objective:** Management aims to determine the optimal quantity of each ingredient to meet the above requirements while minimizing costs. **Task:** Formulate a linear programming model to address this optimization problem, ensuring all nutritional and cost conditions are satisfied.
Transcribed Image Text:**Slim-Down Manufacturing: Strawberry Shake Nutritional Overview** Slim-Down Manufacturing produces a range of nutritionally complete, weight-reduction beverages. Among these is a strawberry shake designed as a complete meal. Below is detailed information on the ingredients used in this shake. | Ingredient | Calories from fat (per tbsp) | Total Calories (per tbsp) | Vitamin Content (mg/tbsp) | Thickeners (mg/tbsp) | Cost (¢/tbsp) | |------------------------|-----------------------------|--------------------------|--------------------------|---------------------|--------------| | Strawberry flavoring | 1 | 50 | 20 | 3 | 10 | | Cream | 75 | 100 | 0 | 8 | 8 | | Vitamin supplement | 0 | 0 | 50 | 1 | 25 | | Artificial sweetener | 0 | 120 | 0 | 2 | 15 | | Thickening agent | 30 | 80 | 2 | 25 | 6 | **Nutritional Requirements:** 1. **Caloric Needs:** - Total calories for the beverage must be between 380 and 420 calories (inclusive). - No more than 20% of the total calories should derive from fat. 2. **Vitamin Content:** - The shake must contain at least 50 milligrams of vitamins. 3. **Flavor and Texture:** - For taste, there must be a minimum of two tablespoons of strawberry flavoring for each tablespoon of artificial sweetener. - To maintain proper thickness, the shake needs exactly 15 milligrams of thickeners. **Objective:** Management aims to determine the optimal quantity of each ingredient to meet the above requirements while minimizing costs. **Task:** Formulate a linear programming model to address this optimization problem, ensuring all nutritional and cost conditions are satisfied.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Practical Management Science
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Business in Action
Business in Action
Operations Management
ISBN:
9780135198100
Author:
BOVEE
Publisher:
PEARSON CO
Purchasing and Supply Chain Management
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…
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.
SEE MORE TEXTBOOKS