Southside Landscapes proposes to plant the flower beds for the historic Earle House gardens. The company uses four patterns. Pattern I uses 40 tulips, 25 daffodils, and 6 boxwood. Pattern II uses 25 tulips, 50 daffodils, and 4 boxwood. Pattern III uses 30 tulips, 40 daffodils, and 8 boxwood. Pattern IV uses 45 tulips, 45 daffodils, and 2 boxwood. The profit for each pattern is $48 for Pattern I,$45 for Pattern II, $55 for Pattern III, and$65 for Pattern IV. Southside Landscape has 1250 tulips, 1600 daffodils, and 195 boxwood available. How many of each pattern should be used to maximize profit?

Solution

VerifiedWe have to use a graphing calculator or a spreadsheet to maximise profit for the given data.

Summary:

$\begin{array}{l c c c c c} \hline & x_1 & x_2 & x_3 & x_4 &\\ & \text{Pattern 1} & \text{Pattern 2} & \text{Pattern 3} & \text{Pattern 4} & \text{Available}\\ \hline \text{Flower 1} & 40 & 25 & 30 & 45 & 1250\\ \text{Flower 2} & 25 & 50 & 40 & 45 & 1600\\ \text{Flower 3} & 6 & 4 & 8 & 2 & 195\\ \hline \text{Profit} & \$48 & \$45 & \$55 & \$65 & \\ \hline \end{array}$

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