Tuckered Outfitters plans to market a custom brand of packaged trail mix. The ingredients for the trail mix will include Raisins, Grain, Chocolate Chips, Peanuts and Almonds costing, respectively, $2.50, $1.50, $2.00, $3.50 and $3.00 per pound. The vitamin, mineral, and protein content of each of the ingredients (in grams per pound) is summarized in the following table along with the calories per pound of ingredient: Vitamins Minerals Protein Calories Raisins Grain 20 7 4 450 10 4 2 160 Chocolate Chips 10 5 1 500 Peanuts 30 9 10 300 Almonds 20 3 1 500 The company would like to identify the least costly mix of these ingredients that provides at least 40 grams of vitamins, 15 grams of minerals, 10 grams of protein, and 600 calories per 2-pound package. Additionally, they want each ingredient to account for at least 5% and no more than 50% of the weight of the package. 1. Formulate the LP model for this problem. 2. Create the spreadsheet model and use Solver to solve the problem. 3. What is the optimal mix, and how much is the total ingredient cost per package?
Tuckered Outfitters plans to market a custom brand of packaged trail mix. The ingredients for the trail mix will include Raisins, Grain, Chocolate Chips, Peanuts and Almonds costing, respectively, $2.50, $1.50, $2.00, $3.50 and $3.00 per pound. The vitamin, mineral, and protein content of each of the ingredients (in grams per pound) is summarized in the following table along with the calories per pound of ingredient: Vitamins Minerals Protein Calories Raisins Grain 20 7 4 450 10 4 2 160 Chocolate Chips 10 5 1 500 Peanuts 30 9 10 300 Almonds 20 3 1 500 The company would like to identify the least costly mix of these ingredients that provides at least 40 grams of vitamins, 15 grams of minerals, 10 grams of protein, and 600 calories per 2-pound package. Additionally, they want each ingredient to account for at least 5% and no more than 50% of the weight of the package. 1. Formulate the LP model for this problem. 2. Create the spreadsheet model and use Solver to solve the problem. 3. What is the optimal mix, and how much is the total ingredient cost per package?
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:Tuckered Outfitters plans to market a custom brand of packaged trail mix. The
ingredients for the trail mix will include Raisins, Grain, Chocolate Chips, Peanuts
and Almonds costing, respectively, $2.50, $1.50, $2.00, $3.50 and $3.00 per
pound. The vitamin, mineral, and protein content of each of the ingredients (in
grams per pound) is summarized in the following table along with the calories per
pound of ingredient:
Vitamins
Minerals
Protein
Calories
Raisins Grain
20
7
4
450
10
4
2
160
Chocolate
Chips
10
5
1
500
Peanuts
30
9
10
300
Almonds
20
3
1
500
The company would like to identify the least costly mix of these ingredients that
provides at least 40 grams of vitamins, 15 grams of minerals, 10 grams of protein,
and 600 calories per 2-pound package. Additionally, they want each ingredient to
account for at least 5% and no more than 50% of the weight of the package.
1. Formulate the LP model for this problem.
2. Create the spreadsheet model and use Solver to solve the problem.
3. What is the optimal mix, and how much is the total ingredient cost per
package?
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