Optimasi univariat

Pengantar Optimasi di Python

Jasmin Ludolf

Content Developer

Contoh: Optimasi di manufaktur

Fungsi objektif:

$P = 40q - 0.5q^2$

Laba berubah terhadap kuantitas.

Fungsi objektif:

$P = 40q - 0.5q^2$

Laba berubah terhadap kuantitas.

Fungsi objektif:

$P = 40q - 0.5q^2$

Turunan: menggambarkan perilaku kemiringan

$\frac{dP}{dq} = 40 - q$

from sympy import symbols, diff, solve


q = symbols('q')

P = 40 * q - 0.5 * q**2

dp_dq = diff(P)

print(f"The derivative is: {dp_dq}")

The derivative is: 40 - 1.0*q

¹ https://docs.sympy.org/latest/index.html

Optimum tercapai saat turunan sama dengan nol

$q$ optimum memenuhi:

$\frac{dP}{dq} = 40 - q = 0$

q_opt = solve(dp_dq)
print(f"Optimum quantity: {q_opt}")

Optimum quantity: [40.0000000000000]

Laba berubah terhadap kuantitas.

Fungsi objektif:

$p = 40q - 0.5q^2$

q_opt = solve(p_prime)
print(f"Optimum quantity: {q_opt}")

Optimum quantity: [40.0000000000000]

Fungsi cekung.

Fungsi cembung.

Laba berubah terhadap kuantitas.

Turunan:

$\frac{dp}{dq} = 40 - q$

Turunan kedua:

$\frac{d^2p}{dq^2} = -1 < 0$

d2p_dq2 = diff(dp_dq)

sol = d2p_dq2.subs('q', q_opt)


print(f"The 2nd derivative is: {sol}")

The 2nd derivative is: -1.0000000000000

Pengantar Optimasi di Python