SOLUTION: Solve the system by graphing
x+y=4
-x+y=2
Solve the system graphing
x-2y=8
x+y=-1
A small company produces both doll houses and sets of doll furniture. The doll hous
Algebra ->
Linear-equations
-> SOLUTION: Solve the system by graphing
x+y=4
-x+y=2
Solve the system graphing
x-2y=8
x+y=-1
A small company produces both doll houses and sets of doll furniture. The doll hous
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Question 119678: Solve the system by graphing
x+y=4
-x+y=2
Solve the system graphing
x-2y=8
x+y=-1
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 requare 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.
You can put this solution on YOUR website! Arrange these equation in the "y" form and plot each one
x+y=4
y = -x + 4
and
-x+y=2
y = x + 2
:
Plot these using x = 4 and x = -4 for both, I assume you know how to do this.
If you don't, email me and I'll go over it
:
You graph should look like this
They intersect at x=1; y=3 so this is the solution. You can confirm this
by substituting x=1 and see that both equation = 3
:
:
Do exactly the same with this one:
Solve the system graphing
x-2y=8
-2y = -x + 8
Y has to be positive, multiply equation by -1
+2y = +x - 8
Y has to have a coefficient of 1; divide equation by 2
y = x - 4
and
x+y=-1
y = -x - 1
:
Plotting this the same way; x=-4 to x=+4
You can see the solution on this one is x=2, y=-3
Substituting these values in the equations will confirm this
:
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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
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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
:
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
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y => 10 is at or above a horizontal line going thru y = 10
:
Look something like this:
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Area of feasibility:
1. At or below the green or purple lines which ever is lowest
2. At or above the horizontal line at y = 10
3. At or to the right of vertical line at x=20
:
Any question about this?
