Expert: Paul Klarreich - 9/23/2007

Question
A small company produces both bouquets and wreaths of dried flowers.  The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours.  The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week.  Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths.

Answer
Questioner:   fred
Category:  Calculus
Private:  No
 
Subject:  algebra
Question:  A small company produces both bouquets and wreaths of dried flowers.  The bouquets take 1 hour of labor to produce, and the wreaths take 2 hours.  The labor available is limited to 80 hours per week, and the total production capacity is 60 items per week.  Write a system of inequalities representing this situation, where x is the number of bouquets and y is the number of wreaths.
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Hi, Fred,

If, as you say:

x = the number of bouquets
y = the number of wreaths

then

x + y <= 60

and

1x = labor needed to produce the bouquets
2y = labor needed to produce the wreaths

and:

x + 2y = labor needed for all the output.

then

x + 2y <= 80

Those are your inequalities.