Working with algebra you must understand why the properties of real numbers are so important. I will demonstrate my solutions to three problems and I will include my mathematical work. Also I will be demonstrating what will work and will not work and what is equal in the inequality. “So the graph of a linear inequality consists of all ordered pairs that satisfy the inequality, and they all lie on one side of the boundary line” (Dugopolski, 2012, Chapter 3.6,). We use a lot of mathematical terms in the real world. Lastly I will show every step and compare why it will work and why not. 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. I will be writing inequality that limits the possible number of maple rockers of each type that can be made, and graph the inequality in the first quadrant.

(b)In my inequality I will be using these variables:
Variable m= the number of modern rocker
Variable c= the number of classic maple rocker
Since classic rocker requires 15 board feet of maple, I will use 15c and since modern rocker requires 12, I will use 12m. I will now write an inequality that limits the number 3000 of board feet of maple lumber for making its classic and modern maple rocking chair.

15c + 12m≤ 3000
I use c as the independent variable (on horizontal axis) and m the dependent variable (on the vertical axis) then I can graph the equation using the intercepts.
15c ≤ 3000 c ≤ 300 the c-intercept is (200, 0).
The m- intercept is found when c=0
12m≤ 3000 m ≤ 250 the m-intercept is (0, 250).

Dealing with this type of inequality equation this is a less than or equal to. The inequality line will be solid, the slope will be downwards and it will move from left to right. I will use the first quadrants because this region of graph is relevant to this problem. I will consider point (75, 150) on my graph. This is inside the shaded area which means the company can use 75 on classic maple rocker and 150 on modern rocker. This is how it would look if they use these items:
75(15) + 150 (12) = 2925 boards feet and have 75 board feet left over. Now looking at these points (95, 160) on the graph, these are outside of the shaded area which means the company can’t make up enough rockers because they don’t have enough board feet. They would run out of board before it even made the classic or modern rocker.
95(15) + 160(12) =3345 feet of board required. This order can’t be filled.

Now look at this point (100, 125). This point is right on the line and means the company will be able to fulfill this order exactly without having any board feet left over.
100(15) + 125(12) = 3000. This order will be filled but there is no room for mistakes or eras.

Apply the linear inequality to solve the following