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
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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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
Content
(per tbsp)
(mg/tbsp)
50
20
100
0
120
80
Ingredient
Strawberry flavoring
Cream
Vitamin supplement
Artificial sweetener
Thickening agent
from fat
(per tbsp)
1
75
0
0
30
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.
Transcribed Image Text: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 Content (per tbsp) (mg/tbsp) 50 20 100 0 120 80 Ingredient Strawberry flavoring Cream Vitamin supplement Artificial sweetener Thickening agent from fat (per tbsp) 1 75 0 0 30 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.
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