July 28, 2013
We know that a classic maple rocker requires 15 board feet of maple and a modern rocker requires 12 board feet of maple. We have “m” which stands for the modern maple rocking chair which is now 12m board feet and the classic chair which is 15c board feet. m= The number of classic maple rocking chair that Ozark Furniture Company has to fill. Therefore, m= 12m (board feet)
c= The number of classic maple chairs that the furniture company has to fill. Therefore c = 15c (board feet)
(a.) The total maple available that was given is 3000 board feet. 15c + 12m = 3000 Inequality that was given with the numbers in place. (b.) Graph for the given inequality.
The inequality is a less than and equal to inequality 15c+12m=3000 will be on the boundary line which lies between the origin to the x and y intercepts. The shaded section is from the line towards the origin and stops at the 2 axis. The point is in the first quadrant and under the shaded area is the solution; Therefore, the ordered pair (x,y) is the point in the shaded region. The Ozark Furniture Company can obtain x number of classic rockers and y number of modern ones. So x-axis shows the number of classic chairs and y-axis shows the number of modern chairs. (c.) Consider the point (40,80). This point is indicating that the company is making 40 classic and 80 modern rocking chairs. Let c=40
Total maple board available is 3000 board ft.
Hence, the total remaining =3000-1560=1440 board feet
So (40,80) is within the region showing that the company can make 40 classic and 80 modern maple rocking chairs using the 1440 board feet of maple to make it. The company can fill the order with no problem. (d) Consider the point (115,180). It is outside the shaded area which means the company could fill this...
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