Constrained example

[Anonymous]

Hello,

Can anybody help me with the calculation of constrained example
y = -x^2+6x-4 subject to x<5 (x less than or equal to 5) (PRM handbook pg no. 211)

Looking forward for the reply.

[Anonymous]

Basicaly, any second order equation y=ax^2 + bx + c have the following roots:

x1= (-b + sqrt(Delta))/(2a)
x2= (-b – sqrt(Delta))/(2a)

where Delta = b^2 – 4ac.

In your example, we have :

x1 = (-6 + sqrt(6^2 -4×4))/(-2) = 3 – sqrt(5) < 5
x2 = (-6 – sqrt(6^2 -4×4))/(-2) = 3 + sqrt(5) > 5

Thus, solution x1 is correct.

[Anonymous]

@Kareem….thanks for your reply
But how can we find value of X here ???
I got x= 0.76 but in handbook its x=3. Can you pls explain me how ???
basically i want to know how to solve inequality example.

thanks in advance

[Anonymous]

Hi Rinky,

Can you please let me know which book you’re refering to ? I have latest PRM handbooks.

Thanks.

[Anonymous]

Hi,

I preparing from PRM handbook. That example is in Numerical optimization pg no. 211.

thanks

[Anonymous]

I have to look in the book because I do not undestand the way you present the question.
Unless you copy exactly the whole question….

[Anonymous]

Hi,

I had a quick look yesterday (btw, page no is 206 in my edition of PRM handbooks bought 6 months ago).

Basically, you have:

y = -x^2+6x-4
= -(x-3)^2 + 5

Thus the function is maximized with x=3, that gives y=5. You can also come to that solution using first order derivation (y’= d(-x^2+6x-4)/dx=-2x+6 => x=3 being the root to the equation)

[Anonymous]

Hey…kareem…thnx a lot for your explanation

regards,
rinky

[Author]

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