A fertilizer wholesaler uses 3 main ingredients in fertilizer mix: Nitrogen, Phosphorus, and Potassium. There are 3 products of mixed fertilizer sold by this retailer: Spring starter, Summer Time, and Winterizer. Net profit per pound of Spring Starters is $0.50, for Summer Time $0.35, and $0.40 for Winterizer. The weekly supply of materials is 19,000 lbs of Nitrogen, 22,000 lbs of Phosphorus, and 16,000 lbs of Potassium. The following table shows the percentage mix of these 3 raw materials for company products: Ingredients Product Nitrogen Phosphorus Potassium Spring Starter 40% 20% 40% Summer Time 30% Winterizer 50% 20% 40% 40% 20% W 1- Identify decision variables, formulate constraints, develop and solve a linear programming model to determine the optimal product mix for maximizing profits. What is the optimal weekly profit, which product is produced more in your optimal solution? 2- Do a sensitivity analysis. Which decision variables have a nonzero reduced cost? What it means and what is the valid range of this reduced cost (allowable increase and decrease)? 3- Which constraints have a nonzero shadow price? What it means for these constraints specifically, and what is the valid range of these shadow prices (allowable increase and decrease)?
A fertilizer wholesaler uses 3 main ingredients in fertilizer mix: Nitrogen, Phosphorus, and Potassium. There are 3 products of mixed fertilizer sold by this retailer: Spring starter, Summer Time, and Winterizer. Net profit per pound of Spring Starters is $0.50, for Summer Time $0.35, and $0.40 for Winterizer. The weekly supply of materials is 19,000 lbs of Nitrogen, 22,000 lbs of Phosphorus, and 16,000 lbs of Potassium. The following table shows the percentage mix of these 3 raw materials for company products: Ingredients Product Nitrogen Phosphorus Potassium Spring Starter 40% 20% 40% Summer Time 30% Winterizer 50% 20% 40% 40% 20% W 1- Identify decision variables, formulate constraints, develop and solve a linear programming model to determine the optimal product mix for maximizing profits. What is the optimal weekly profit, which product is produced more in your optimal solution? 2- Do a sensitivity analysis. Which decision variables have a nonzero reduced cost? What it means and what is the valid range of this reduced cost (allowable increase and decrease)? 3- Which constraints have a nonzero shadow price? What it means for these constraints specifically, and what is the valid range of these shadow prices (allowable increase and decrease)?
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:A fertilizer wholesaler uses 3 main ingredients in fertilizer mix: Nitrogen, Phosphorus, and Potassium. There are 3 products of mixed fertilizer sold by
this retailer: Spring starter, Summer Time, and Winterizer. Net profit per pound of Spring Starters is $0.50, for Summer Time $0.35, and $0.40 for
Winterizer. The weekly supply of materials is 19,000 lbs of Nitrogen, 22,000 lbs of Phosphorus, and 16,000 lbs of Potassium. The following table
shows the percentage mix of these 3 raw materials for company products:
Ingredients
Product
Nitrogen
Phosphorus Potassium
Spring Starter 40%
20%
40%
Summer Time 30%
Winterizer
50%
20%
40%
40%
20%
W
1- Identify decision variables, formulate constraints, develop and solve a linear programming model to determine the optimal product mix for
maximizing profits. What is the optimal weekly profit, which product is produced more in your optimal solution?
2- Do a sensitivity analysis. Which decision variables have a nonzero reduced cost? What it means and what is the valid range of this reduced cost
(allowable increase and decrease)?
3- Which constraints have a nonzero shadow price? What it means for these constraints specifically, and what is the valid range of these shadow prices
(allowable increase and decrease)?
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