Question 99726: A small company produces both doll houses and doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of doll furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalitites.
I think I have found the system of inequalitites. I am not sure if they are correct though.
3x + 8y < 400; x + y < 100; x > or equal to 20; y > or equal to 10
I also came up with these points for the graph
(20,10); (66,24); (23,66); (64,26) Is this all correct?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A small company produces both doll houses and sets of doll furniture. The doll houses take 3 hours of labor to produce, and the furniture sets take 8 hours. The labor available is limited to 400 hours per week, and the total production capacity is 100 items per week. Existing orders require that at least 20 doll houses and 10 sets of furniture be produced per week. Write a system of inequalities representing this situation, where x is the number of doll houses and y is the number of furniture sets. Then graph the system of inequalities.
:
This problem came up a few weeks ago, I submitted this then.
:
I saw the 1st coordinate was right (20,10) and assumed the rest were right, however on a closer look the corners of the area of feasibility should be:
20,10; 20,42.5; 80,20; and 90,10, as you can see by the graph
x = number of doll houses; y = furniture sets
:
The labor constraint:
3x + 8y =< 400
Arrange in the general (y=) form so we can plot the graph
8y =< 400 - 3x
y =< (400/8) - (3/8)x
y =< 50 - (3/8)x
:
The production constraint:
x + y =< 100
y =< 100 - x
:
Min house constraint:
x => 20
:
Min furniture constraint
y => 10
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Plot the Labor equation; I assume you know how to substitute for x and find y
x | y
-------
0 | 50
8 | 47
32 | 38
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Plot the production restraint
x | y
------
0 |100
20 | 80
50 | 50
:
x => 20 is at or to the right of a vertical line going thru x=20
:
y => 10 is at or above a horizontal line going thru y = 10
:
Look something like this: You have to draw in the vertical line at x = 20
:
Area of feasibility:
1. At or below the green or purple lines which ever is lowest
2. At or above the horizontal line
3. At or to the right of vertical line at x=20 which you have to draw in
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