Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 750 units of vitamin C and 76 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 46 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 30 units of vitamin C and also 8 units of vitamin E. The total supplement of these two foods must be at most 27 ounces. Unfortunately, food I contains 35 units of cholesterol per ounce and food II contains 26 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. x = number of ounces of Food I v y = number of ounces of Food II v Maximize v x F = (objective function) Subject to (total ounces of food) (units of vitamin C) (units of vitamin E) x 0, y > 0 (nonnegativity constraint)

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 33E
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Formulate a linear programming problem that can be used to solve the following question.
An individual needs a daily supplement of at least 750 units of vitamin C and 76 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each
ounce of food I contains 46 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 30 units of vitamin C and also 8 units of vitamin E. The total
supplement of these two foods must be at most 27 ounces. Unfortunately, food I contains 35 units of cholesterol per ounce and food II contains 26 units of cholesterol per
ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized.
X = number of ounces of Food I v
y = number of ounces of Food II v
Maximize
X F =
(objective function)
Subject to
(total ounces of food)
(units of vitamin C)
(units of vitamin E)
X>
х о, у>
X 0 (nonnegativity constraint)
Transcribed Image Text:Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 750 units of vitamin C and 76 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 46 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 30 units of vitamin C and also 8 units of vitamin E. The total supplement of these two foods must be at most 27 ounces. Unfortunately, food I contains 35 units of cholesterol per ounce and food II contains 26 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. X = number of ounces of Food I v y = number of ounces of Food II v Maximize X F = (objective function) Subject to (total ounces of food) (units of vitamin C) (units of vitamin E) X> х о, у> X 0 (nonnegativity constraint)
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