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The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phos- phate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phos- phate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phos- phate, and 2 ounces of potassium while minimizing cost. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.

The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phos- phate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phos- phate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phos- phate, and 2 ounces of potassium while minimizing cost. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
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1. Formulate a linear model (clearly state decision variables, objective function, and constraints) 2. Find optimal solutions using graphical techniques as shown in class PowerPoint slides. 3. Find slack or surplus variables at each optimal solution. 4. Show your work to get all points.
Transcribed Image Text:1. Formulate a linear model (clearly state decision variables, objective function, and constraints) 2. Find optimal solutions using graphical techniques as shown in class PowerPoint slides. 3. Find slack or surplus variables at each optimal solution. 4. Show your work to get all points.
#3 The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phos- phate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phos- phate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phos- phate, and 2 ounces of potassium while minimizing cost. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.
Transcribed Image Text:#3 The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phos- phate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phos- phate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phos- phate, and 2 ounces of potassium while minimizing cost. a. Formulate a linear programming model for this problem. b. Solve this model by using graphical analysis.
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