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.
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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.
{{{graph(400,300,-5,40,-5,30,(-14/9)x+(260/9))}}}
Use the cost equation as your objective function.
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Cheers,
Stan H.