Small Doll Furniture
Lines/slopes and a big Word problem. How do I solve?
1)
A line passing through (2, –4) and (4, y) is perpendicular to a line with slope: -2/13 Find the value of y.
2)
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.
Hi,
#1 A line perpendicular to a line with a slope of -2/13 would have the negative reciprocal, 13/2, as its slope. Putting this into the slope formula, you get:
13…..y + 4
—-.=.——–
2……..4.-.2
13…..y + 4
—-.=.——–
2……..2
26 = 2y + 8
18 = 2y
9 = y
y = 9 <== answer
#2 Making at least 20 doll houses means you'd make 20 or more, so that's x ≥ 20.
Making at least 10 sets of furniture means you'd make 10 or more, so that's y ≥ 10
Since there is a limit of 100 total items, x + y ≤ 100.
Since there are 400 hours maximum to work and it takes 3 hours per doll house and 8 hours per furniture set, then hours are limited by 3x + 8y ≤ 400.
The inequalities for this problem are:
x ≥ 20
y ≥ 10
x + y ≤ 100
3x + 8y ≤ 400
They intersect at (20,10), (20,42.5), (80,20), and (90,10).
If you were looking for maximum profit, it would occur at one of these points, but you'd have to have the profit formula before you could determine it.
I hope that answers your inequality questions!! 
Black Shopping Channel (“BSC”) dollhouse furniture
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