SOLUTION: A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths takes 2 hours. The labor available is limited to

Question 120914: A small company produces both bouquets and wreaths of dried flowers. The bouquets take 1 hour of labor to produce, and the wreaths takes 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. Then graph the system of inequalities.
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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
:
Labor constraint:
1x + 2y =< 80
2y =< -x + 80
y =< -.5x + 40; divided equation by 2 ( this is the form we want for graphing)
:
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:

Area of feasibility would be at or below the lowest line (Positive values only)
:
Did this make sense to you? Any questions?

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