Tell Me Your Question...

A landscaping contractor uses a combination of two brands of fertilizers each containing different amounts of phosphates and

nitrates. Brand A has 4 pounds of phosphate per package and 2 pounds of nitrate per package. Brand B has 6 pounds of phosphate

per package and 5 pounds of nitrate per package. A certain lawn requires a mixture of at least 24 pounds of phosphates and at least 16

pounds of nitrates. Brand A costs $6.99 and a package of brand B costs $17.99. How much of each should be purchased for the lowest

cost but meeting the minimum requirement?

Pulling Out Important Values

A landscaping contractor uses a combination of two brands of fertilizers each containing different amounts of phosphates and

nitrates. Brand A has 4 pounds of phosphate per package and 2 pounds of nitrate per package. Brand B has 6 pounds of phosphate

per package and 5 pounds of nitrate per package. A certain lawn requires a mixture of at least 24 pounds of phosphates and at least 16

pounds of nitrates. Brand A costs $6.99 and a package of brand B costs $17.99. How much of each should be purchased for the lowest

cost but meeting the minimum requirement?

Make Sense of What We Have

Blue = Variables Orange = Phosphate Values

Red = Nitrate Values Pink = Cost Values

Applying Values

A > 0 B > 0

4A + 6B > 242A + 5B > 16

C = 6.99A + 17.99B

Graphing Your Values

See Handout for GraphSee Handout for Graph

Unknown Point B

4A + 6B = 24+ -2(2A + 5B = 16) -4B = -8 B = 2

2A + 5B = 162A + 5(2) = 16 2A + 10 = 16

2A = 6 A= 3

Calculating Profits

C = 6.99A + 17.99B

6.99(0) + 17.99(4) = $71.966.99(3) + 17.99(2) = $56.956.99(8) + 17.99(0) = $55.92

Profit Statement

To minimize cost by $55.92 and still meeting the minimum requirement, purchase 8 bags of Brand

A and 0 bags of Brand B.