Question 110539
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. 
:
Let x = no. of bouquets; y = no. of wreaths
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Labor constraint:
1x + 2y =< 80
2y =< -x + 80
y =< -.5x + 40; divided equation by 2 ( this is the form we want for graphing)
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Production capacity constraint:
x + y =< 60
y =< -x + 60
:
Then graph the system of inequalities.
Plot two points for each:
y = -.5x + 40
 x | y
-------
 0 | 40
50 | 15 
and
y = -x + 60
 x | y
--------
 0 | 60
50 | 10
:
Plot and draw these two graphs, should look like this:
 {{{ graph( 300, 200, -10, 80, -10, 80, -.5x+40, -x+60) }}}
Area of feasibility would be at or below the lowest line (Positive values only)
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Did this make sense to you? Any questions?