February 16, 2014
This week we are learning about two-variable inequalities as they pertain to algebraic expressions. The inequality can be graphed to show the values included in and excluded from a given range of numbers. Solving for inequalities such as these is a critical skill in many trades which can save or cost a company a lot of time and money. Ozark Furniture Company can obtain at most 3000 board feet of maple lumber for making its classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. Write an inequality that limits the possible number of maple rockers of each type that can be made, and graph the inequality in the first quadrant. First I must assign a variable to each type of rocker Ozark Furniture makes. Let c = the number of classic rockers
Let m = the number of modern rockers
It takes 15 board feet of lumber for each classic rocker so I will use 15c in my equation. Likewise, I will use 12m for the 12 board feet of lumber in the modern rocker. The maximum amount of lumber Ozark can obtain is 3000 board feet. Therefore, my equation will look like this: 15c + 12m ≤ 3000
If I call c the independent variable (on the horizontal axis) and m the dependent variable (graphed on the vertical axis) then I can graph the equation using the intercepts. The c-intercept is determined when m = 0:
15c ≤ 3000
c ≤ 200
The c-intercept is (200,0).
The m-intercept is found when c = 0:
12m ≤ 3000
m ≤ 250
The m-intercept is (0, 250).
Since this inequality is “less than or equal to”, the graphed line will be solid, sloping downward from left to right within the first quadrant of the graph. The shaded section will cover the area from the line towards the origin, stopping at the respective axes.
Consider the point (50,100) on my graph. It is well...
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