TP[p_]=
p(a
-bp
e
)(2LT-
2
T
)
2LT
-
pv(a
-bp
e
)(2LT-
2
T
)1+
-kTf
βe

-αTf
e
(1+β)2LT
-
hr(a
-bp
e
)(3L
2
T
-2
3
T
)
6LT
-
Bc(a
-bp
e
)(2LT-
2
T
)1+
-kTf
βe
(
γTf
e
-1)
A
-αTf
e
γ2LT
-
Kk-Ks 
T 
-
ε 
T
cr
(a
-bp
e
)(2LT-
2
T
)
2L
+cs
(a
-bp
e
)(2LT-
2
T
)1+
-kTf
βe

-αTf
e
(1+β)2L
+ch
(a
-bp
e
)(3L
2
T
-2
3
T
)
6L
 +cg
(
-bp
ae
)(2LT-
2
T
)1+
-kTf
βe
(
γTf
e
-1)
A
-αTf
e
γ2L
+cn+cl​​(*Computethefirstderivative*)​​dTPdp=D[TP[p],p]​​​​(*Solveforp*)​​solution=Solve[dTPdp0,p]​​​​(*Simplifythesolution*)​​simplifiedSolution=Simplify[solution]