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Linear Programming Project

Nutrition Facts & Linear ProgrammingAn Algebra II Project
by

Joseph Breen

on 8 October 2012

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Transcript of Linear Programming Project

Nutrition Facts and Linear Programming Joseph Breen
Ms. Vande Creek
Algebra II Honors The Facts Vanilla Gatorade
Nutrition Shake Peach Propel
Fitness Water I have had a long-lasting cold and the doctor recommended to maximize the amount of Vitamin C in my monthly diet. Therefore, I chose two drinks containing Vitamin C (Propel Fitness Water and Gatorade Nutrition Shakes) and added them to my diet. The doctor recommended at least 120g of carbohydrates. I also can't exceed 80g of fat or 1672 calories. How many bottles of Propel and cans of Gatorade should I drink? Objective and Constraints Variables: p (Propel Fitness Water)
g (Gatorade Nutrition Shake)
C: amount of Vitamin C Objective Function: C=6p+60g The Graph (0,58) (0,40) (4,10) (4,0) (2,0) I solved my system to find the corner points using the graphing method. It worked out that all of my points came to be whole numbers, so there was no algebra involved whatsoever. Finding the Maximum Corner Point Evaluations g p 0 5+7= (cc) image by anemoneprojectors on Flickr C=6p+60g 0 0 0 40 58 2 4 4 10 6(40)+60(0)=240 6(58)+60(0)=348 6(o)+60(2)=120 6(0)+60(4)=240 6(10)+60(4)=300 Maximum: 58 bottles of Propel, 0 of Gatorade (gives the highest amount of Vitamin C at 348mg) Conclusion In order to maximize the amount of Vitamin C in my diet without exceeding the constraints, I would need to drink 58 bottles of Propel Peach Fitness Water per month. This will result in 348mg of Vitamin C. Extensions Linear programming was developed by George Dantzig, between 1947 and 1949. During World War II, Dantzig was on one of the numerous planning teams. After many hours of studying, he realized that these plans could be expressed as a system of linear inequalities. He related the armed forces' goals to an objective function. He used the objective function, to find the maximum and minimum optimal solutions. He deduced that these solutions could be found at the corner points of the feasible region (the reason where all of the inequalities overlap). After his amazing discovery, Dantzig was able to solve multiple problems. The first problem he ever solved required nine equalities. It was a way to minimize the cost of a diet, while still maintaining a healthy amount of each nutrient. The solution required 120 men, each using the most advanced calculator of time. As computers and computer software began to develop, Dantzig's discovery became less tedious and more widely used.
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