Janice and Raymund run a day care for preschoolers. They are trying to decide what to feed the children for lunches. They would like to keep their costs down, but also need to meet the nutritional requirements of the children. They have already decided to go with peanut butter and jelly sandwiches, and some combination of graham crackers, milk, and orange juice. The nutritional content of each food choice and its cost are given in the table below: Food Item Calories from Total Calories Vitamin C Protein (g) Cost (in PhP) Fat 10 75 |(mg) 3 5 Bread (1 slice) Peanut butter |(1 tbsp) Strawberry jelly (1 tbsp) Graham 70 100 4 4 50 3 7 20 60 1 8 cracker (1 cracker) Milk (1 cup) Juice (1 cup) 70 150 100 2 120 15 35 8 The nutritional requirements are as follow. Each child should receive between 400 and 600 calories. No more than 30% of the total calories should come from fat. Each child should consume at least 60 milligrams (mg) of vitamin C and 12 grams of protein. For practical reasons, each child needs exactly 2 slices of bread, at least twice as much peanut butter as jelly, and at least 1 cup of liquid (milk and/or juice). Formulate a LP model for this problem in order to minimize the cost while at the same time meeting the nutritional requirements.
Janice and Raymund run a day care for preschoolers. They are trying to decide what to feed the children for lunches. They would like to keep their costs down, but also need to meet the nutritional requirements of the children. They have already decided to go with peanut butter and jelly sandwiches, and some combination of graham crackers, milk, and orange juice. The nutritional content of each food choice and its cost are given in the table below: Food Item Calories from Total Calories Vitamin C Protein (g) Cost (in PhP) Fat 10 75 |(mg) 3 5 Bread (1 slice) Peanut butter |(1 tbsp) Strawberry jelly (1 tbsp) Graham 70 100 4 4 50 3 7 20 60 1 8 cracker (1 cracker) Milk (1 cup) Juice (1 cup) 70 150 100 2 120 15 35 8 The nutritional requirements are as follow. Each child should receive between 400 and 600 calories. No more than 30% of the total calories should come from fat. Each child should consume at least 60 milligrams (mg) of vitamin C and 12 grams of protein. For practical reasons, each child needs exactly 2 slices of bread, at least twice as much peanut butter as jelly, and at least 1 cup of liquid (milk and/or juice). Formulate a LP model for this problem in order to minimize the cost while at the same time meeting the nutritional requirements.
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...
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Transcribed Image Text:Janice and Raymund run a day care for preschoolers. They are trying to decide what to
feed the children for lunches. They would like to keep their costs down, but also need
to meet the nutritional requirements of the children. They have already decided to go
with peanut butter and jelly sandwiches, and some combination of graham crackers,
milk, and orange juice. The nutritional content of each food choice and its cost are
given in the table below:
Food Item
Calories from Total Calories
Vitamin C
Protein (g)
Cost (in PhP)
Fat
(mg)
Bread (1 slice)
10
70
3
5
Peanut butter
75
100
4
4
(1 tbsp)
Strawberry
jelly (1 tbsp)
Graham
50
3
20
60
8.
cracker (1
cracker)
Milk (1 cup)
Juice (1 cup)
70
150
8
15
100
120
1
35
The nutritional requirements are as follow. Each child should receive between 40o0 and
600 calories. No more than 30% of the total calories should come from fat. Each child
should consume at least 60 milligrams (mg) of vitamin C and 12 grams of protein. For
practical reasons, each child needs exactly 2 slices of bread, at least twice as much
peanut butter as jelly, and at least 1 cup of liquid (milk and/or juice).
Formulate a LP model for this problem in order to minimize the cost while at the same
time meeting the nutritional requirements.
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