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 u

Algebra ->  Graphs -> 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 u      Log On


   



Question 1086217: 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?

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm using x in place of A and y in place of B,
3x%2B4y%3C=100
280x%2B180y%3E=5200
y%3E=4
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So then graphing the constraints shows the feasible region and the vertices of the region A,B, and C.
Check the cost and nutrition level for each vertex.
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So it looks like,
A=x=28 and B=y=4 provides the best nutrition level of 8560 and stays within the cost limit.