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Algebra 2: Linear Programming Moose Meals Betsey Davis Mathematics & Science Center www.cpaws.org/park-integrity/ park- wardens.html

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Moose Meals B. Davis 2005 Mathematics & Science Center Moose Meals tMoose eat terrestrial stuff daily t kilograms a Moose eat aquatic stuff daily a kilograms whyfiles.org/shorties/ 069predator_prey/ www.learnnc.org/.../ $FILE/moose.jpg www.greatplains.o rg/resource/ 1999/ndmnrngp/12 2.gif www.durham.net/~ssh-chin/ arrowhead.jpg

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Moose Meals B. Davis 2005 Mathematics & Science Center Amounts www.state.wy.us/.../home_page/ spring/pictures/moose.jpg Each day one moose can only process 32 kilograms, so, a + t < 32

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Moose Meals B. Davis 2005 Mathematics & Science Center Amounts www.state.wy.us/.../home_page/ spring/pictures/moose.jpg a + t < 32 a t

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Moose Meals B. Davis 2005 Mathematics & Science Center Calories www.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

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Moose Meals B. Davis 2005 Mathematics & Science Center Calories www.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 a t

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Moose Meals B. Davis 2005 Mathematics & Science Center Calories www.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 t

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Moose Meals B. Davis 2005 Mathematics & Science Center Sodium 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

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Moose Meals B. Davis 2005 Mathematics & Science Center Sodium 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

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Moose Meals B. Davis 2005 Mathematics & Science Center Sodium detnews.com/2002/outdoors/ 0201/18/d09-389782.htm Let’s add to our graph.15a + 0 t > 1.9 t 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.

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Moose Meals B. Davis 2005 Mathematics & Science Center webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg Summary Moose : 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

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Moose Meals B. Davis 2005 Mathematics & Science Center webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg Summary In algebra: a + t < 32 193a + 772 t > 11000.15a + 0 t > 1.9 t a

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Moose Meals B. Davis 2005 Mathematics & Science Center webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg Summary t 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.

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Moose Meals B. Davis 2005 Mathematics & Science Center Long live the moose! mbgnet.mobot.org/sets/taiga/ animals/pict/4.

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