An exercise of linear programming model formulation Slim-Down Manufacturing makes a line of nutritionally complete, weight-r eduction beverages. One of their products is a strawberry shake which is desig ned to be a complete meal. The strawberry shake consists of several ingredien ts. Some information about each of these ingredients is given below. Thickener Calories from F Total Calorie Vitamin Conte Cost S Ingredient at S nt ($/tbs (mg/tbs (per/tbsp) (per/tbsp) (mg/tbsp) p) p) Strawberry flavori 1 50 20 10 ng Cream 75 100 8 Vitamin suppleme 50 1 25 nt Artificial sweetene 120 2 15 r Thickening agent 30 80 25 6. The nutritional requirements are as follows. The beverage must total between 380 and 420 calories (inclusive). No more than 20 percent of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin c ontent. For taste reasons, there must be at least 2 tablespoons (tbsp) of straw berry flavoring for each tablespoon of artificial sweetener. Finally, to maintain proper thickness, there must be exactly 15 mg of thickeners in the beverage. Management would like to select the quantity of each ingredient for the bevera ge which would minimize cost while meeting the above requirements. Can you formulate a linear programming model for this problem?
An exercise of linear programming model formulation Slim-Down Manufacturing makes a line of nutritionally complete, weight-r eduction beverages. One of their products is a strawberry shake which is desig ned to be a complete meal. The strawberry shake consists of several ingredien ts. Some information about each of these ingredients is given below. Thickener Calories from F Total Calorie Vitamin Conte Cost S Ingredient at S nt ($/tbs (mg/tbs (per/tbsp) (per/tbsp) (mg/tbsp) p) p) Strawberry flavori 1 50 20 10 ng Cream 75 100 8 Vitamin suppleme 50 1 25 nt Artificial sweetene 120 2 15 r Thickening agent 30 80 25 6. The nutritional requirements are as follows. The beverage must total between 380 and 420 calories (inclusive). No more than 20 percent of the total calories should come from fat. There must be at least 50 milligrams (mg) of vitamin c ontent. For taste reasons, there must be at least 2 tablespoons (tbsp) of straw berry flavoring for each tablespoon 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 bevera ge which would minimize cost while meeting the above requirements. Can you formulate a linear programming model for this problem?
Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:An exercise of linear programming model formulation
Slim-Down Manufacturing makes a line of nutritionally complete, weight-r
eduction beverages. One of their products is a strawberry shake which is desig
ned to be a complete meal. The strawberry shake consists of several ingredien
ts. Some information about each of these ingredients is given below.
Thickener
Calories from F Total Calorie Vitamin Conte
Cost
S
Ingredient
at
S
nt
($/tbs
(mg/tbs
(per/tbsp)
(per/tbsp)
(mg/tbsp)
p)
p)
Strawberry flavori
1
50
20
10
ng
Cream
75
100
8
Vitamin suppleme
50
1
25
nt
Artificial sweetene
120
2
15
r
Thickening agent
30
80
25
6.
The nutritional requirements are as follows. The beverage must total between
380 and 420 calories (inclusive). No more than 20 percent of the total calories
should come from fat. There must be at least 50 milligrams (mg) of vitamin c
ontent. For taste reasons, there must be at least 2 tablespoons (tbsp) of straw
berry flavoring for each tablespoon 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 bevera
ge which would minimize cost while meeting the above requirements.
Can you formulate a linear programming model for this problem?
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