SOLUTION: A nursery uses two brands of fertilizer for rose bushes. Brand A costs $3 per pound and provides 280 units of nutrients per pound. Brand B costs $4 per pound and provides 180 units
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Question 92178: A nursery uses two brands of fertilizer for rose bushes. Brand A costs $3 per pound and provides 280 units of nutrients per pound. Brand B costs $4 per pound and provides 180 units of nutrients per pound.
CONSTRAINTS: The nursery spends $100 or less for fertilizer and wants to provide at least 5200 units of nutrients. Because brand B contains a special nutrient that brand A does not, the nursery uses at least 4 pounds of brand B.
How many pounds of each should the nursery use to minimize cost?
You can put this solution on YOUR website! A nursery uses two brands of fertilizer for rose bushes.
Brand A costs $3 per pound and provides 280 units of nutrients per pound.
Brand B costs $4 per pound and provides 180 units of nutrients per pound.
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CONSTRAINTS: The nursery spends $100 or less for fertilizer and wants to provide at least 5200 units of nutrients.
Because brand B contains a special nutrient that brand A does not, the nursery uses at least 4 pounds of brand B.
How many pounds of each should the nursery use to minimize cost?
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Cost Inequality: 3A + 4B <=100
Nutrient Inequality: 280A + 180B >=5200
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Constraints:
B>=4
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Solve where you can for B:
B <=(-3/4)A+25
B >=(-280/180)A + (5200/180)
B >=4
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Plot the last two on an A-B coordinate system
Find the coordinates of the vertices of the enclosed area.
Evaluate the cost function with those coordinates to find
the minimum cost.
Use the cost equation as your objective function.
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Cheers,
Stan H.
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