746 WordsFeb 5, 20133 Pages

Two Variable Inequality
Robin Bettasso
Mat 221
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*…show more content…*

So, c = 200 and m = 100.
So, 15c + 12m = 15(200) + 12(100) = 3000 + 1200 = 4200.
Total board maple available = 3000 board feet.
Hence, extra maple required = 4200 – 3000 = 1200 board feet.
So, (200, 100) point, which is out of the region showing that the company is making 200 classic and 100 modern maple rocking chairs and need 4200 board feet of maple. In this case the company needs 1200 board feet of maple. So, company cannot fill this order with the available maple. iii) Consider the point (100, 125).
This point is indicating that the company is making 100 classic and 125 modern maple rocking chairs.
So, c = 100 and m = 125.
So, 15c + 12m = 15(100) + 12(125) = 1500 + 1500 = 3000.
Total board maple available = 3000 board feet.
So, here the company has exact amount of required maple.
So, (100, 125) point, which is exactly on the line showing that the company is making 100 classic and 125 modern maple rocking chairs and need to be very careful because company has exact amount of maple available to complete this order. So, company can complete the order.
f) Here the order is of 125 classic rocking chairs and 175 modern rocking chairs. In terms of point we can show this condition as (125, 175).
So, we have c = 125 and m = 175.
So, 15c + 12m = 15(125) + 12(175) = 1875 + 2100 = 3975 board feet.
Total maple available = 3000 board feet.
So, Ozark Furniture will need 3975 – 3000 = 975 board feet of lumber.
So, Ozark Furniture is not

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