Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 440 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 40 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 30 ounces. Unfortunately, food I contains 34 units of cholesterol per ounce and food II contains 33 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. x = ---Select--- number of ounces of Food I number of units of vitamin C y = ---Select--- number of units of vitamin E number of ounces of Food II ---Select--- Minimize Maximize F = (objective function) Subject to (total ounces of food) (units of vitamin C) (units of vitamin E) x ---Select--- ≤ < > ≥ = 0, y ---Select--- ≤ > = ≥ < 0 (nonnegativity constraint)
Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 440 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 40 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 30 ounces. Unfortunately, food I contains 34 units of cholesterol per ounce and food II contains 33 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. x = ---Select--- number of ounces of Food I number of units of vitamin C y = ---Select--- number of units of vitamin E number of ounces of Food II ---Select--- Minimize Maximize F = (objective function) Subject to (total ounces of food) (units of vitamin C) (units of vitamin E) x ---Select--- ≤ < > ≥ = 0, y ---Select--- ≤ > = ≥ < 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 440 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 40 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 30 ounces. Unfortunately, food I contains 34 units of cholesterol per ounce and food II contains 33 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized.
x = ---Select--- number of ounces of Food I number of units of vitamin C
y = ---Select--- number of units of vitamin E number of ounces of Food II
| ---Select--- Minimize Maximize | F =
|
(objective function) |
| Subject to |
|
(total ounces of food) |
|
|
(units of vitamin C) | |
|
|
(units of vitamin E) | |
| x ---Select--- ≤ < > ≥ = 0, y ---Select--- ≤ > = ≥ < 0 | (nonnegativity constraint) |
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