Question 1155593
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A diet specialist tells patient to add oranges and apples to her diet for Vitamin A, Vitamin B, and Vitamin C. 

A kg (kilogram) of oranges contributes 8 grams of Vitamin C, 6 grams of Vitamin B, and 2 grams of Vitamin A, while 

a kg of apples contributes 3 grams of Vitamin A and 6 grams of Vitamin B. 

A kg of oranges costs $1.95 and a kg of apples costs $2.99. 

The patient has to meet a minimum requirement of 22 grams of Vitamin A, 33 grams of Vitamin B, and 16 grams of Vitamin C. 

She should avoid taking more than 73 grams of Vitamin A and 64 grams of Vitamin B to avoid side effects such as nausea. 

Formulate a linear programming problem to help the patient choose the ideal fruit mix for their diet.
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<pre>
Let x be the amount of oranges, and let y be the amount of apples for optimal diet (in kilograms).


Then the objective function to minimize is the price  P = 1.95x + 2.99y  dollars.


The constraints are


22 <= 2x + 3y <= 73   (the amount of vitamin A, in grams)

33 <= 6x + 6y <= 64   (the amount of vitamin B, in grams)

16 <= 8x              (the amount of vitamin C, in grams)

x >= 0,  y >= 0.
</pre>

The setup is just completed.


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To see many problems solved by the Linear Programming method, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/misc/Solving-minimax-problems-by--the-Linear-Programming-method.lesson>Solving minimax problems by the Linear Programming method</A> 

in this site.


Also, &nbsp;look into the solutions of other similar problems in the archive to this forum under the links


https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1148776.html

https://www.algebra.com/algebra/homework/Inequalities/Inequalities.faq.question.1142000.html 

https://www.algebra.com/algebra/homework/Sequences-and-series/Sequences-and-series.faq.question.1137172.html

https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1136382.html

https://www.algebra.com/algebra/homework/Coordinate-system/Coordinate-system.faq.question.1134444.html

https://www.algebra.com/algebra/homework/Graphs/Graphs.faq.question.1131906.html

https://www.algebra.com/algebra/homework/coordinate/word/Linear_Equations_And_Systems_Word_Problems.faq.question.1131043.html

https://www.algebra.com/algebra/homework/word/finance/Money_Word_Problems.faq.question.1129285.html

https://www.algebra.com/algebra/homework/Linear-equations/Linear-equations.faq.question.1123217.html   (!)

https://www.algebra.com/algebra/homework/playground/test.faq.question.1112482.html

https://www.algebra.com/algebra/homework/Finance/Finance.faq.question.1102103.html



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In order for the formulation be <U>precisely correct</U>, from the common sense point of view,

it must say for what time period this diet is designed (a day, a week, and so on . . . )


It does not play any role in the setup and/or in the solution,

but is NECESSARY PART from the common sense point of view.