SOLUTION: Could someone please help me this problem is from a worksheet and I really do not understand how to do this thank you in advance for all the help. A small company produces both

Question 92254: Could someone please help me this problem is from a worksheet and I really do not understand how to do this thank you in advance for all the help.
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 avaiable is limited to 400 hours per week,and the total production capacity is 100 items per week.Existing order requare that at 20 doll houses and 10 sets of furniture be produced per week.write a system of inequqlites representing this sitution,where x is the number of doll houses and y is the number of furniture sets.Then graph the system of inequalities.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
This same problem came up a few months ago, here is what I submitted then,
perhaps it will help you.
:
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.
:
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
:
Plot the Labor equation; I assume you know how to substitute for x and find y
x | y
-------
0 | 50
8 | 47
32 | 38
:
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
:
Any question about this?

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