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
Oct 25, 2015

#2**+10 **

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. :)

Melody
Oct 25, 2015

#1**+15 **

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)

Melody
Oct 25, 2015

#2**+10 **

Best Answer

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. :)

Melody
Oct 25, 2015