Ozark Furniture
Lori Pope
MAT221: Introduction to Algebra
Instructor: Kemba Chambers
December 2, 2013

Ozark Furniture Ozark furniture has 3000 board feet of maple lumber in stock. In order to make classic maple rockers they need 15 board feet of maple lumber. In order to make a modern rocker they need 12 board feet of maple lumber. So we need to process an inequality and graph it in order to be sure that we have enough of the maple lumber in stock to prepare orders. The first step is to define what variables that I will be using in my inequality. So let’s say c = the number of classic maple rockers and let m= the number of modern rockers. Because each of the classic maple rockers require 15 board feet, I will use 15c, and because each modern rocker requires 12 board feet, I will use 12m. Remember I am limited to the amount of maple lumber which is 3000 board feet. My inequality that I will use will look like this: 15c+12m< 3000. Next, we will call c the independent variable on my horizontal axis and m the dependent variable on the vertical axis. By doing this we can graph the equation using the intercepts. The C-intercept is found when m=0 15c< 3000 c< 200
So what we are saying is that the C-intercept is (200, 0)
The M-intercept is found when c=0 12< 3000 m< 250
So what we are saying here is that the M-intercept is (0, 250) I will be using a solid line because of the “less than or equal to” inequality. Also notice that the solid line will be sloping down as it moves from left to right. The region that is important to the problem given is limited to the first quadrant which is a shaded section from the line towards the origin and slopes at the two axis. Now let’s say that we look at a point (75,100) on the graph. This is in the shaded area which then means that the Ozark Company could fill the order of 75 classic rockers and 100 modern rockers. If this many rockers where made it would look like this: 75(15) + 100(12) =2325 board feet of maple lumber. We would still have 675 board feet of maple lumber left over. Let’s say we look at it another way, our points would be (100,150). This is outside of the shaded area which then means that the Ozark Company could not make up enough of both kinds of rocking chairs to fill the order. If this many rockers where made it would look like this: 100(15) + 150 (12) =3300 board feet of maple lumber. But we only have 3000, so we would not be able to fill this order because we would be 300 board feet of maple lumber short. A customer comes into Ozark Company and wants 125 classic rocking chairs and 175 modern rocking chairs, will the Ozark Company be able to fill the order? We will go back and look at the graph equation and see if (125,175) fall inside or outside the shaded area. By looking at the graph (125, 175) falls outside of the graph so Ozark Company would not be able to fill the order. If we filled this order it would look like this: 125(15) + 175(12) = 3975 - We would be 975 boards short of completing our order. Using variables for a given item and using inequality formulas can help companies that make items to order. This formula can tell them whether they can complete an order with the materials they have or if the order is too big for them to fulfill.

Reference
Dugopolski, M. (2012). Elementary & Intermediate Algebra. New York: McGraw Hill Companies.