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Submitted By run32bit
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Dik: Q = 10 K1/2 L1/2 C = w + r 1000 = 30 L + 40 K 1000 – 30 L – 40 K = 0

Dit : L dan K……? Jumlah Output untuk menghasilkan nilai maximum..?

Jawab:
Fungsi Lagrange Z = 10 K1/2 L1/2 + λ (1000 – 30 L – 40 K) Z = 10 L1/2 K1/2 + 1000 λ – 30 λ L – 40 λ K
Maka, dZ= 5 L1/2 K-1/2 – 40 λ ................................................ 1 dL

Z = 10 K1/2 L1/2 + 1000 λ – 30 λ L – 40 λ K
Maka, dZ = 5 K1/2 L-1/2 – 30 λ ................................................ 2 dK dZ = 5 L-1/2 K1/2 – 30 λ ................................................ 2 dK

Z = 10 L1/2 K1/2 + 1000 λ – 30 λ L – 40 λ K
Maka, dZ= 1000 – 30 L – 40 K .............................................. 3 d λ

Persamaan 1 dan 2

5 L1/2 K-1/2 – 40 λ x 3 ...................1
5 L-1/2 K1/2 – 30 λ x 4 ...................2

15 L1/2 K-1/2 – 120 λ
20 L-1/2 K1/2 – 120 λ -

15 L1/2 K-1/2 = 20 L-1/2 K1/2
15 L1/2 = 20 K1/2 K1/2 L1/2

15 L1/2 L1/2 = 20 K1/2 K1/2 15 L = 20 K L = 20 K 15 L = 4 K 3
Substitusikan nilai L = 4 K ke Persamaan 1000 – 30 L – 40 K = 0 3

Maka 1000 – 30 L – 40 K = 0 1000 – 30.4K – 40 K = 0 3 1000 – 40 K – 40 K = 0 1000 – 80 K = 0 1000 = 80 K 1000 = K 80 12,5 = K

Lalu substitusikan K=12,5 ke persamaam L = 4 K 3 L = 4 .12,5 3 L = 16,67

Jadi nilai L = 16,67 dan K = 12,5

Jumlah Output untuk menghasilkan nilai maksimum adalah
Q = 10 K1/2 L1/2
Q = 10 √12,5 . √16,67
Q =10 . 3,535 . 4,082
Q = 144,32

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