constrained optimisation

[unborn magnet]

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[nocturne loom]

your system from $\nabla\mathcal{L}=0$ is $\begin{cases}0.4m-\lambda=0\5-\lambda=0\m+n=q\end{cases}$

[tough oracle]

Omegabet_

[nocturne loom]

which does have an equation with n, namely n=q-m

you're assuming q is a known constant here

[hardy sedge]

This gives $c(q) = 5q - \frac{125}{4}$

[tough oracle]

George

[hardy sedge]

This doesn't make sense since for m, n, q = 0, c(q) should be 0

[dire carbon]

write L(m,n) instead of L(x,y)

unless m = m(x), n = n(x), which is not specified

[nocturne loom]

when q is 0, you're minimizing m^2/5 + 5n subject to n=-m

so you're minimizing $\frac{1}{5}m^2-5m$ as $m$ ranges, which has a vertex at $(12.5,-125/4)$

[tough oracle]

Omegabet_

[nocturne loom]

which is consistent with that c(q)

[hardy sedge]

Thank you

.close