Homework Help: Got a question with substitution?

1. Apr 19, 2005

MRAI

Using the Substitution method, find the maximum value of

4x-2xy+3y subject to the constraint 4x-y=2

I can do the 1st part:

4x-y=2--->
4x-2=y

substitute this into the original equation:
4x-2x(4x-2)+3(4x-2)

Hope that right so far! but dont know where to go from there? any one could help plz?

thanks ;)

2. Apr 19, 2005

CartoonKid

then you differentiate wrt x and equal to zero to find max/min

3. Apr 19, 2005

MRAI

what do u mean by wrt?

4. Apr 19, 2005

HallsofIvy

"wrt" : "with respect to"
CartoonKid was assuming this was a calculus problem. The standard method for solving "maximum- minimum" problems in calculus is to differentiate and set the derivative equal to 0. But since you apparently weren't aware of that, I suspect this is not a calculus problem!

If you multiply y= 4x-2x(4x-2)+3(4x-2) out, you get a quadratic. If you are doing problems like this, I presume you know how to complete the square to find the vertex of the graph which, in this problem, gives you the maximum value.

So: multiply this out, then complete the square.

5. Apr 19, 2005

dextercioby

This method is totally counterproductive...The method discovered by Lagrange is much more elegant...

Daniel.

6. Apr 19, 2005

Theelectricchild

But one would need a rather intermediate mathematical background to use them...