The first step is much like any other step; we must attain a understanding of what we are working with. The text states that “Ozark Furniture Company can obtain at most 3,000 board feet of maple lumber for making its classic and modern maple rocking chairs. A maple classic rocker requires 15 board feet of maple, and a maple 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.”

With the information from the text we can easily make the maple classic rocking chairs as the variable labeled “x” and the maple modern rocking chairs will be labeled as the variable of “y”. Now we must look to see how many materials are needed for each of the builds. It appears that the classic chair requires 15 feet of maple wood so we will use “15x” as the first term of the inequality. Now to look at the modern rocker, this chair requires 12 feet of maple wood. So much like the classic term we will use “12y”. The company is able to use 3,000 feet of board to create chairs so we will use the inequality of 15x + 12y ≤ 3000 where ≤ means using all of the boards which the company can get. From here we will move 15x to the right side the equation using subtraction on both sides which will create 12y ≤ 3000 – 15y. We will not divide the equation by 12 on both sides and simplify which will create y ≤ 250 – (5/4)x.

Now we must find the x-intercept. Using y ≤ 250 – (5/4)x, we will plug in “0” into “y” which will achieve 0 ≤ 250 – (5/4)x. We will now move -5/4x to the left side using addition on both sides to create 5/4x ≤ 250. Now we will divide both sides by 5/4 to get x≤200. This will show that the company can only create 200 classic rocking chairs max. The X coordinate will be (200,0). Now we will find the y-intercept. We will use y ≤ 250 – 5/4x and