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Algebra 2: Linear Programming Moose Meals

Moose require a balanced diet consisting of terrestrial and aquatic foods to thrive. Each moose can process up to 32 kilograms of food daily while needing a minimum of 11,000 calories and 1.9 grams of sodium each day. The consumption of aquatic and terrestrial foods varies, with their aquatic diet generally providing higher sodium content. These dietary needs can be illustrated using linear programming to establish a feasible intake range, ensuring moose meet their nutritional requirements effectively.

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Algebra 2: Linear Programming Moose Meals

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

  2. Moose Meals • Moose eat terrestrial stuff daily t kilograms whyfiles.org/shorties/ 069predator_prey/ www.greatplains.org/resource/ 1999/ndmnrngp/122.gif Moose eat aquatic stuff dailya kilograms www.learnnc.org/.../ $FILE/moose.jpg www.durham.net/~ssh-chin/ arrowhead.jpg Moose Meals B. Davis 2005 Mathematics & Science Center

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

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

  5. 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 Moose Meals B. Davis 2005 Mathematics & Science Center

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

  7. t 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 Moose Meals B. Davis 2005 Mathematics & Science Center

  8. Sodium www.lm.liverpool.k12.ny.us/.../ periodicchart/sodium.html • We have looked at volume of food and energy from food. Now we examine the sodium requirement of moose. www.northstar.k12.ak.us/schools/ awe/moose/moosefood.html Moose Meals B. Davis 2005 Mathematics & Science Center

  9. Sodium www.lm.liverpool.k12.ny.us/.../ periodicchart/sodium.html • 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.northstar.k12.ak.us/schools/ awe/moose/moosefood.html So, .15a + 0 t > 1.9 Moose Meals B. Davis 2005 Mathematics & Science Center

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

  11. 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 webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg In algebra: a + t < 32 193a + 772 t > 11000 .15a + 0 t > 1.9 Moose Meals B. Davis 2005 Mathematics & Science Center

  12. t a Summary In algebra: a + t < 32 193a + 772 t > 11000 .15a + 0 t > 1.9 webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg Moose Meals B. Davis 2005 Mathematics & Science Center

  13. t a Summary 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. webhome.crk.umn.edu/clubs/wildlife/ Components/Moose004.jpg About (12.5,19.5) About (24,8) About (12.5,10.5) Moose Meals B. Davis 2005 Mathematics & Science Center

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

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