Expert: Paul Klarreich - 10/30/2008

Question
Chapter 7- Linear Programming

Sorry, I forgot to ask this question. Write a system of inequalities that describes the conditions.

A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates and 1 unit of fat. Every package must provide at least 7 units of protein, at least 10 units of carbohydrates, and no more than 9 units of fat. Let x be the number of ounces of fruit and y the number of ounces of nuts to be used in each package.

Answer
Questioner:   Jeffrey
Category:  Advanced Math
Private:  No
 
Subject:  Discrete Mathematics
Question:  Chapter 7- Linear Programming

Sorry, I forgot to ask this question. Write a system of inequalities that describes the conditions.

A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates and 1 unit of fat. Every package must provide at least 7 units of protein, at least 10 units of carbohydrates, and no more than 9 units of fat. Let x be the number of ounces of fruit and y the number of ounces of nuts to be used in each package.
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Hi, Jeffrey,

After you write:
LET x be the number of ounces of fruit to be used in ONE package.

LET y be the number of ounces of nuts to be used in ONE package.

the next word is

THEN, as in:

THEN 1x = the number of units of protein in a package FROM FRUIT
THEN 2x = the number of units of carbs   in a package FROM FRUIT
THEN 1x = the number of units of fat     in a package FROM FRUIT

THEN 1y = the number of units of protein in a package FROM NUTS
THEN 1y = the number of units of carbs   in a package FROM NUTS
THEN 1y = the number of units of fat     in a package FROM NUTS

followed by the word

AND, as in

AND 1x + 1y = the total units of protein in a package.
AND 2x + 1y = the total units of carbs   in a package.
AND 1x + 1y = the total units of fat     in a package.

and finally, you write your sentences, using  

'>=' for the phrase 'at least', and
'<=' for the phrase 'no more than'

That should do it.