Monday, December 6, 2010

Ch. 3.4 Linear Programming

For my ch. 3.4 Linear programming project, i came up with my own problem: Ms. Noonan and the ESA group is trying to protect Sausal creek from non-native species, we plan on restoring, and protecting 300square feet of dirt to help Sausal creek prevent erosion, 300feet square feet of dirt are invaded by non-native invasive plants. We will first remove all the non-native plants and then plant two native plants: Native Ivies and Gulf Fritillaries, Each native ivy covers 1.5 square feet. Each Gulf Fritillary will cover .3 square feet. Each plants cost $5 and Ms. Noonan can only spend $3,000. Write constraints and graph the feasible reason.

For my project,
Let I = the # of Native Ivies (y-axis)
Let F = the # of Gulf Fritillaries (x-axis)

The Constraints are:
I is greater than or equal to 0 (shown in red)
F is greater than or equal to 0 (shown in Green)
1.5I + .3F is less than or equal to 300 (Shown in orange)
5I + 5F is less than or equal to 3000 (shown in blue)

I then Graphed the Constraints,

I then got all the graphs put onto one big one to find the feasible region,
the intersecting feasible region is indicated in green, it is a quadrilateral
With the vertices:
(0,0), (0,200), (600,0), (500,100)

and the point such as: (200,100) satisfies all the constraints,
meaning that Ms, Noonan can buy 100 Fritillaries and 200 native Ivies to help restore sausal creek without exceeding her spending limit $3,000

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