Got a question with substitution?

  • Thread starter Thread starter MRAI
  • Start date Start date
  • Tags Tags
    Substitution
AI Thread Summary
The discussion revolves around using the Substitution method to maximize the expression 4x - 2xy + 3y under the constraint 4x - y = 2. The initial steps involve substituting y with 4x - 2 into the original equation. Participants suggest differentiating the resulting expression with respect to x to find critical points for maximum or minimum values. However, there is a debate on whether this problem is calculus-based or not, with some advocating for the use of the Lagrange method as a more elegant solution. Ultimately, the conversation highlights different approaches to solving optimization problems in mathematics.
MRAI
Messages
5
Reaction score
0
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 don't know where to go from there? anyone could help please?

thanks ;)
 
Physics news on Phys.org
then you differentiate wrt x and equal to zero to find max/min
 
what do u mean by wrt?
 
"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.
 
This method is totally counterproductive...The method discovered by Lagrange is much more elegant...

Daniel.
 
But one would need a rather intermediate mathematical background to use them...
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
Back
Top