January 20, 2013
a) Let ‘c’ be the number of classic maple rocking chairs and ‘m’ be the number of classic maple rocking chairs that Ozark Furniture Company make. b) Here we have given that a classic maple rocker requires 15 board feet of maple, and a modern rocker requires 12 board feet of maple. We have ‘c’ classic maple rocker, so total maple required for classic maple rocker chair = 15c board feet. And we have ‘m’ modern maple rocker, so total maple required for classic maple rocker chair = 12m board feet. We have total maple available is 3000 board feet.
Hence we can show this condition as:
15c + 12m ≤ 3000.
This is the inequality which is showing the given situation. c) Graph for this inequality:
d) Here this is a less than and equal to inequality, so we need to take the area which is below to the line 15c + 12m = 3000 and this will be a solid line on the boundaries. The region lies between origin to x and y – intercepts. Each point which is in the first quadrant and under the shaded area is a solution for the given inequality. So, if (x, y) is a point in the shaded region then Ozark Furniture Company can obtain x number of classic and y number of modern maple rocking chairs. So, x – axis is showing number of classic maple rocking chairs and y – axis is showing the number of modern maple rocking chairs. i) Consider the point (50, 100).
This point is indicating that company is making 50 classic and 100 modern maple rocking chairs. So, c = 50 and m = 100.
So, 15c + 12m = 15(50) + 12(100) = 750 + 1200 = 1950.
Total board maple available = 3000 board feet.
Hence, total remaining maple = 3000 – 1950 = 1050 board feet. So, (50, 100) point, which is within the region showing that the company is making 50 classic and 100 modern maple rocking chairs and using 1950 board feet of maple. In this case total waste of maple is 1050 board feet. So, the company can fill the order easily. ii) Consider...