A company blends nitrogen and phosphorous to produce two types of fertilizers. Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound. Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound. The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound.Assuming that all fertilizer produced can be sold, determine the optimal blending plan for the company. What is the maximum profit?Suppose the company could acquire 1,000 pounds more of either nitrogen or phosphorous. Which should it choose? What would be the resulting impact on profit?
A company blends nitrogen and phosphorous to produce two types of fertilizers. Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound. Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound. The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound.Assuming that all fertilizer produced can be sold, determine the optimal blending plan for the company. What is the maximum profit?Suppose the company could acquire 1,000 pounds more of either nitrogen or phosphorous. Which should it choose? What would be the resulting impact on profit?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section: Chapter Questions
Problem 58P
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A company blends nitrogen and phosphorous to produce two types of fertilizers. Fertilizer 1 must be at least 50% nitrogen and sells for $55 per pound. Fertilizer 2 must be at least 55% phosphorous and sells for $45 per pound. The company can purchase up to 9000 pounds of nitrogen at $20 per pound and up to 12,000 pounds of phosphorous at $12 per pound.
Assuming that all fertilizer produced can be sold, determine the optimal blending plan for the company. What is the maximum profit?
Suppose the company could acquire 1,000 pounds more of either nitrogen or phosphorous. Which should it choose? What would be the resulting impact on profit?
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