# Variables

The Ozark Furniture Company has 3000 board feet of maple lumber for making classic and modern maple rocking chairs. A classic rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple.
The variables that are needed in the inequality:
c = the number of classic rockers
m = the number of modern rockers
Each classic rocker requires 15 board feet of lumber we will use 15c, and since each modern rocker requires 12 board feet of lumber, let’s use 12m. The total amount of lumber which will be used is limited to 3000 board feet. The inequality looks like this: 15c +12m ≤ 3000
If c is the independent variable and m the dependent variable, then we can graph the equation using the intercepts.
The c intercept is found when m = 0:
15c ≤ 3000;
Then divide both sides by 15;
c ≤ 200;
The c-intercept is (200, 0).
The m - intercept is found when c = 0:
12m ≤ 3000;
Then divide both sides by 12;
m ≤ 250
The m-intercept is (0, 250).
A less than or equal to inequality is found.   The line will slope downward from left to right. The region of the graph is in the first quadrant and the shaded section is from the line towards the origin and stops at the two axes.
Using the coordinates (90, 120), this will fall inside the shaded area.   This means that the company would be able to complete an order of 90 classic rockers and 120 modern rockers.
See this example: 15(90) + 12(120) = 2790 board feet and still have 210 board feet left over.
Now let’s consider points (100, 160) on the graph.   These would not fall in the shaded area.   This means the company would not be able to make enough of both types of rockers to complete the order.
See this example: 15(100) + 12(160) = 3420 board feet required. This means the company could not fill the order because it does not have enough board feet.
Finally, let’s look at coordinates (100, 125). These points would fall on the line.   This means that the company is able to make enough of the...