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A farmer wants to plant a crop in the spring and needs to fertilize a field. There are two brands of fertilizer to choose

 

A farmer wants to plant a crop in the spring and needs to fertilize a field. There are two brands of fertilizer to choose from, Super-gro and Crop-quick. Each brand yields a specific amount of Nitrogen (N) and Phosphate (P) per bag, as follows: Nitrogen Phosphate Brand (lb./bag) (lb./bag) Super-gro 2 4 Crop-quick 4 3 The farmer's field requires at least 16 pounds of nitrogen and 24 pounds of phosphate. Super-gro costs $6 per bag, and Crop-quick costs $3. a) The farmer wants to know how many bags of each brand to purchase in order to minimize the total cost of fertilizing. b) Solve the model you had formulated in Part(a) using Graphical Method. c) Determine the range of the ratio of bags of nitrogen to bags of phosphate that will keep the the optimum obtained in Part(b).

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