By graphing the systems of constraints, find the values of x and y that maximize the objective function.
x+y≤8
2x+y≤10
x≥0
y≥0
maximum for N = 100x+40y
answers:
(0,0)
(5,0)
(0,8)
(2,6)
PayPay sent me a private message asking if i could try to explain some more.
Paypay doesn't understand the moving orange line.
It is a strange concept I think, I am not surprised that you did not understand and I am pleased that you asked about it.
I have changed the graph just a little. (I just added the names of the points)
https://www.desmos.com/calculator/4w3xa3c3yy
x+y≤8
2x+y≤10
x≥0
y≥0
Now the dark quadrilateral in the middle is the region that x and y must lie in.
The vertices of this region are (0,0), (5,0), (0,8), (2,6)
Lets just substitute these points into the equation 100x+40y = constant
(0,0) 100*0+40*0=0 The constant would be 0
(5,0) 100*5+40*0=500 The constant would be 500
(0,8) 100*0+40*8=320 The constant would be 320
(2,6) 100*2+40*6=200+240=440 The constant would b e 440
So the biggest constant is 500. It happens whe x=5 and y=0 (5,0)
So you can do this without understanding the orange line but it would be good if you understood the line so I will try to explain.
Now, what has this got to do with the moving orange graph???
The orange line is the graph of 100x+40y = a constant
What you are finding is the biggest constant that this equation can equal (within the given region.)
The slider is N
So you can make N bigger or smaller. I have set it to move between 0 an 1000.
So you can move the orange line, by changingthe value of N. You want the biggest possible N value so that at least some part of the line falls in the given region. When N is 500 only one point of the line is in the region. That point is (5,0). If N is bigger than 500 then no point on the line will fall in the restricted region. SO the biggest possible value of N within the given restrictions is 500 and N is 500 at the point (5,0)
Have a good think about this because it is a concept that can help you with a variety of problems. :)
Hi PayPay
By graphing the systems of constraints, find the values of x and y that maximize the objective function.
x+y≤8
2x+y≤10
x≥0
y≥0
Here is your graph.
https://www.desmos.com/calculator/lmiz3pkgw2
The constraints for a quadrilateral where the vertices are the 4 points that you have been given
I have also graphed 100x+40y=N where N can take on a sliding range of values.
It is orange and if you move the slider the orange line will move.
The greatest value of N will occur on the last corner befor the orange line leaves the constraint region. Hopefully you can see that happen at (5,0)
maximum for N = 100x+40y
Alternatively, if you substitute those answer values into the N equation, you will find that N is greatest at (5,0)
answers:
(0,0)
(5,0)
(0,8)
(2,6)
PayPay sent me a private message asking if i could try to explain some more.
Paypay doesn't understand the moving orange line.
It is a strange concept I think, I am not surprised that you did not understand and I am pleased that you asked about it.
I have changed the graph just a little. (I just added the names of the points)
https://www.desmos.com/calculator/4w3xa3c3yy
x+y≤8
2x+y≤10
x≥0
y≥0
Now the dark quadrilateral in the middle is the region that x and y must lie in.
The vertices of this region are (0,0), (5,0), (0,8), (2,6)
Lets just substitute these points into the equation 100x+40y = constant
(0,0) 100*0+40*0=0 The constant would be 0
(5,0) 100*5+40*0=500 The constant would be 500
(0,8) 100*0+40*8=320 The constant would be 320
(2,6) 100*2+40*6=200+240=440 The constant would b e 440
So the biggest constant is 500. It happens whe x=5 and y=0 (5,0)
So you can do this without understanding the orange line but it would be good if you understood the line so I will try to explain.
Now, what has this got to do with the moving orange graph???
The orange line is the graph of 100x+40y = a constant
What you are finding is the biggest constant that this equation can equal (within the given region.)
The slider is N
So you can make N bigger or smaller. I have set it to move between 0 an 1000.
So you can move the orange line, by changingthe value of N. You want the biggest possible N value so that at least some part of the line falls in the given region. When N is 500 only one point of the line is in the region. That point is (5,0). If N is bigger than 500 then no point on the line will fall in the restricted region. SO the biggest possible value of N within the given restrictions is 500 and N is 500 at the point (5,0)
Have a good think about this because it is a concept that can help you with a variety of problems. :)