WI08ma1bineq-story

WI08ma1bineq-story - Math 1b A story where a nonnegative...

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Math 1b — A story where a nonnegative solution is required January 16, 2009 An ounce of food substances F 1 ,F 2 3 4 provides the following percentages of a student’s minimum daily requirements of three nutrients: carbohydrates, vitamin X, and mineral Y. The table also gives the price per ounce of these foods. carbohydrates vitamin X mineral Y cost per oz. F 1 5% 5% 25% $0.20 F 2 3% 20% 1% $0.23 F 3 10% 0% 10% $0.15 F 4 8% 10% 2% $0.20 You are going on a day trip and will need to carry these foods with you, but you can carry at most one pound of food since you will have your textbooks and laptop to carry too. Your budget is $2.50. How much of each food should you take in order to satisfy your daily requirements of nutrients, not hurt your back, and stay within your budget? Or is this impossible??? We let x i denote the number of ounces of food F i , i =1 , 2 , 3 , 4, that you will carry. Our requirements are 0 . 05 x 1 +0 . 03 x 2 . 10 x 3 . 08 x 4 1 0 . 05 x 1 . 20 x 2 . 10 x 4 1 0 . 25 x 1 . 01 x 2 . 10 x 3 . 02 x 4 1 x 1 + x 2 + x 3 + x 4 16 0 . 20 x 1 . 23 x 2 . 15 x 3 . 20 x 4 2 . 5 with all x i 0. These are inequalities, not equations, but we make equations by intro-
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WI08ma1bineq-story - Math 1b A story where a nonnegative...

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