Substituting the partial derivatives yields:
σP1 σ [(1-σ)(1 -7)(1 -T4) - γσ(1 - T1 )] [σP∙1-σT∙-7(1-L)]
+σ77P1-σΘ*(1 - Ti)L
+(σ-1+7)[[σP*1-σT* -7(1 -L)][σP1-σT- γL] - 72ΘΘ*(1 -L)L]
(14.3)
+7σ
(1-TA )
l-7
-Y
(i-ta)1-y p-γ
(1 - Ti) (σP1-σT - γL + γσΘ(1 -L))
+ (1 - a)(1 - 7)(1 - '/'7θ!∣ -L)
= 0,
[7(1 -L)-σP*1-σT*] [σP1-σ (1 -Ta-T)+ 7L]
P γ +7 2ΘΘ*(1-L)L
P*7 = P*1-σ7σ (1 - TA)1-γ (1 - Ta)7 (1-L)Θ.
Substituting (14.4) in (14.3) and simplifying yields:
(14.4)
τ _ . — τ* _
TA,Opt = 1 A,Opt =
σ
(14)
while resubstituting (14) in (14.4) or (14.3) yields for T1,θpt and TI,θpt the
following non-linear equation system:
7θ*l + p7p*1-σ-γ - 1 -σTI
σ - 1 1 - Ti
(1-7 )P ∙1-σ + 7 (1-L) + '* 1 =0,
σ-1
7 Θ(1 - L) 1-σ-7 1 - σT*
σ - 1 + P P - Tif
(1 -7)P1-σ+7L +
7σ(1 -L)Θ
σ - 1
(15)
23
= 0.
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