Inequalities can be applied in several aspects of life. In our discussion this week we will be applying the properties of inequality to the production of maple rockers by the Ozark Furniture Company. This company can obtain 3000 board feet of maple lumber to make 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. Our first goal is to write an inequality that limits the possible number of maple rockers of each type that can be made with the total board feet. Then we must graph this inequality in the first quadrant. c I will be using c as the variable for the classic rocker. m The variable for the modern maple rocker will be m. t The total board feet that the company can acquire is represented by t. c + m < t I have shown the inequality using the variables.
15c + 12m < 3000 This is the inequality with the required amount and total board feet available.

Using c as the independent variable which is on the horizontal axis and m as the dependent variable on the vertical axis, we can graph the equation.
The c intercept is found 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)

When graphing this inequality the line will be solid and sloping downward from left to right. The shaded section is from the line to the origin stopping at the two axes because it is restricted to the first quadrant. If you consider the point (75,125) it would be in the shaded area. That means the Ozark Furniture Company could make 75 classic rockers, 125 modern rockers, and would still have 375 square board feet of maple left over.
75(15) + 125(12) = 2625 If you consider the point (125,125) it would not be in the shaded area. This means that if 125 classic rockers and 125 modern rockers were ordered, the Ozark Furniture Company would be 375 square board feet of maple short of fulfilling this order.
125(15) + 125(12) = 3375 If you consider the point (100,125) it would be right on the line. The company could make 100 classic rockers and 125 modern rockers, but there would be no maple board left so there would be no room for mistakes.
100(15) + 125(12) = 3000 If an order of 175 modern rocking chairs and 125 classic rocking chairs was placed, the company would be unable to fulfill the order. They will be 975 board feet of oak shy. 125,175 will fall outside the shaded area on the graph. 125(15) + 175(12) = 3975 I very much appreciated this assignment. I can always understand the concepts of math better, when I am applying them to a real life scenario. Dugopolski, M. (2012). Elementary and Intermediate Algebra, 4th Edition. New York: McGraw-Hill.