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Math help, Please!?
Ozark furniture company can obtain at most 3000 board feet of maple lumbar for making 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. Write in inequality that limits the possible number of maple rockers of each type that can be made, and graph the inequality in the first quadrant.
7 Answers
Let x = number of classic rockers and
y = number of modern rockers, then
15x + 12y <= 3000
To graph this inequality, just pretend it is a line.
15x + 12y = 3000
Find the x- and y-intercepts. Plot them. Connect the intercepts.
Then find out where to shade the line by using a test point. I would suggest (0,0) as your test point.
Restrict it to the first quadrant. Do you know why it is restricted to the first quadrant? Since x and y are how many boards that are needed, and you cannot have a negative amount of boards. So x and y must be greater than or equal to zero. This is what the first quadrant represents.
y = number of modern rockers, then
15x + 12y <= 3000
To graph this inequality, just pretend it is a line.
15x + 12y = 3000
Find the x- and y-intercepts. Plot them. Connect the intercepts.
Then find out where to shade the line by using a test point. I would suggest (0,0) as your test point.
Restrict it to the first quadrant. Do you know why it is restricted to the first quadrant? Since x and y are how many boards that are needed, and you cannot have a negative amount of boards. So x and y must be greater than or equal to zero. This is what the first quadrant represents.
The most classic rockers that can be made is 3000/15 = 200.
Therefore 0<= x <=200 where x = number of classic rockers.
The most modern rockers that can be made is 3000/12 = 250
Therefore 0 <= y <= 250 where y = number of modern rockers
If you want to be able to make both types then:
15x +12y <= 3000,
or 5x + 4y <= 1000
y <= (1000-5x)/4 =-(5/4)x + 250
So you have a line starting at (0,250) on the y-axis and going to the point (200,0) on the x-axis
Anything below this line and above the x-axis satisfies the inequality.
Therefore 0<= x <=200 where x = number of classic rockers.
The most modern rockers that can be made is 3000/12 = 250
Therefore 0 <= y <= 250 where y = number of modern rockers
If you want to be able to make both types then:
15x +12y <= 3000,
or 5x + 4y <= 1000
y <= (1000-5x)/4 =-(5/4)x + 250
So you have a line starting at (0,250) on the y-axis and going to the point (200,0) on the x-axis
Anything below this line and above the x-axis satisfies the inequality.
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