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 1086427: 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. 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?
Found 2 solutions by stanbon, ikleyn:
Answer by stanbon(75887) (Show Source): 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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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
Units Inequality: 280A + 180B >= 5200
Weight Inequality B >= 4
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Graph the inequalities;
A <= -4B + 100
A >= -180B + 5200
B >= 4
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Identify the appropriate vertices.
Determine which coordinate pair minimizes cost.
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Cheers,
Stan H.
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Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
.
On solving minimax problems with linear constraints by the linear programming method see the lesson
- Solving minimax problems by the Linear Programming method
in this site.
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