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Two-Variable Inequality

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. I will be using c as the variable for the classic rocker. I will be using m as the variable for the modern maple rocker will be m. 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.

The maximum amount of Classics is = 3000 ⁄ 15 = 200

The maximum amount of Moderns is = 3000 ⁄ 12 = 250

The graph below shows this, where the connecting line should be solid

and the solution region (shaded) is below and including the line.

Modern

    ↑

      |

   250   •

      |     \

      |░  \

      |░ \

      |░░ \

      |░░░\

      |░░░  \

      |░░░░   \

      |░░░░░\

      |░░░░░   \

      |░░░░░░  \

      |░░░░░░░\

      |░░░░░░░░\

      0 |——————•——> Classic

    0      200

 The slope = (-  250 ⁄ 200)  and the  y_intercept = 250

          M  ≤  (-  250 ⁄ 200)  •  C  +  250

          M  ≤  (-  5 ⁄ 4)  •  C  +  250

Reference

Dugopolski, M. (2012). Elementary and intermediate algebra (4th ed.). New York, NY: McGraw-Hill Publishing.