1. 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?

2. 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?

3. Make Sense of What We Have Blue = Variables Orange = Phosphate Values Red = Nitrate Values Pink = Cost Values

4. Applying Values A > 0 B > 0 4A + 6B > 24 2A + 5B > 16 C = 6.99A + 17.99B

5. Graphing Your Values See Handout for Graph

6. Unknown Point B 4A + 6B = 24 + -2(2A + 5B = 16) -4B = -8 B = 2 2A + 5B = 16 2A + 5(2) = 16 2A + 10 = 16 2A = 6 A= 3

7. Calculating Profits C = 6.99A + 17.99B 6.99(0) + 17.99(4) = $71.96 6.99(3) + 17.99(2) = $56.95 6.99(8) + 17.99(0) = $55.92

8. 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.