Algebra 2: Linear ProgrammingAlgebra 2: Linear ProgrammingMoose MealsMoose Meals

Betsey Davis

Mathematics & Science Center

www.cpaws.org/park-integrity/ park-wardens.html

Moose Meals B. Davis 2005 Mathematics & Science Center

Moose MealsMoose Meals

• Moose eat terrestrial stuff daily

tt kilograms

Moose eat aquatic stuff daily

a a kilograms

whyfiles.org/shorties/ 069predator_prey/

www.learnnc.org/.../ $FILE/moose.jpg

www.greatplains.org/resource/ 1999/ndmnrngp/122.gif

www.durham.net/~ssh-chin/ arrowhead.jpg

Moose Meals B. Davis 2005 Mathematics & Science Center

AmountsAmounts

www.state.wy.us/.../home_page/ spring/pictures/moose.jpg

• Each day one moose can only process 32 kilograms,

• so,

• a + t < 32

Moose Meals B. Davis 2005 Mathematics & Science Center

AmountsAmounts

www.state.wy.us/.../home_page/ spring/pictures/moose.jpg

• a + t < 32

-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

-15.0

-10.0

-5.0

5.0

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t

Moose Meals B. Davis 2005 Mathematics & Science Center

CaloriesCalorieswww.state.wy.us/.../home_page/ spring/pictures/moose.jpg

• Moose needs at least 11000 calories a day

• a gives 193 per kilo

• t gives 4 times as much or

• 4x193 t = 772 t per kilo

• so…

• 193a + 772 t > 11000

Moose Meals B. Davis 2005 Mathematics & Science Center

CaloriesCalorieswww.state.wy.us/.../home_page/ spring/pictures/moose.jpg

• Let’s add calories requirements to the kilogram limitations already on the graph

• 193a + 772 t > 11000

-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

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t

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Moose Meals B. Davis 2005 Mathematics & Science Center

CaloriesCalorieswww.state.wy.us/.../home_page/ spring/pictures/moose.jpg

193a + 772 t > 11000

Here we didn’t bother to shade everything greater than the line.

Instead we only shaded where the new information overlaps the old kilogram information.

a-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

-15.0

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t

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Moose Meals B. Davis 2005 Mathematics & Science Center

SodiumSodium

• We have looked at volume of food and energy from food. Now we examine the sodium requirement of moose.

www.lm.liverpool.k12.ny.us/.../ periodicchart/sodium.html

www.northstar.k12.ak.us/schools/ awe/moose/moosefood.html

Moose Meals B. Davis 2005 Mathematics & Science Center

SodiumSodium

• A moose needs 1.9 grams of sodium per day.

• Aquatic food, a, provides .15 grams of sodium per kilo

• Terrestrial food, t, has minimal sodium.

www.lm.liverpool.k12.ny.us/.../ periodicchart/sodium.html

www.northstar.k12.ak.us/schools/ awe/moose/moosefood.html

So,

.15a + 0 t > 1.9

Moose Meals B. Davis 2005 Mathematics & Science Center

SodiumSodium

detnews.com/2002/outdoors/ 0201/18/d09-389782.htm

Let’s add to our graph

.15a + 0 t > 1.9

-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

-15.0

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t

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a

Again, let us not shade everything to the right of the line. Let us just shade where the new region overlaps the yellow and green.

Moose Meals B. Davis 2005 Mathematics & Science Center

webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg

SummarySummaryMoose :

can process 32 kilograms of food daily

their food comes from land and water

they need 11000 calories per day

they need 1.9 grams of sodium per day

In algebra:a + t < 32

193a + 772 t > 11000

.15a + 0 t > 1.9

Moose Meals B. Davis 2005 Mathematics & Science Center

webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg

SummarySummary

In algebra:a + t < 32193a + 772 t > 11000

.15a + 0 t > 1.9

-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

-15.0

-10.0

-5.0

5.0

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20.0

25.0

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35.0

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45.0

t

-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

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a

Moose Meals B. Davis 2005 Mathematics & Science Center

webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg

SummarySummary

-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

-15.0

-10.0

-5.0

5.0

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25.0

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45.0

t

-10.0-5.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0

-15.0

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-5.0

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a

About (24,8)

About (12.5,19.5)

About (12.5,10.5)

Examining the corner points of the triangular feasible region tells us that a moose needs to consume daily:

between 12.5 to 24 kilo of aquatic food

and between 8 and 19.5 kilo of land food to survive.

Moose Meals B. Davis 2005 Mathematics & Science Center

Long live the moose!Long live the moose!

mbgnet.mobot.org/sets/taiga/ animals/pict/4.