Advanced mathematical modeling

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from sympy import *
n=symbols('n')
y=1250*(2-exp(-(n-5000)**2))
func1=diff(y,n)
print(func1)
stag=solve(diff(y,n),n)
print(" The stagnation point of this function is ",stag)
func2=diff(y,n,2)
print(func2)
print(func2.evalf(subs={
    n:5000}))
func2.evalf(sub={
    n:5000})>0
y.evalf(sub={
    n:5000})

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import scipy.optimize as opt
from scipy import fmin
import numpy as np
def func0(cost,x,a):

    return cost*x*(2-exp(-(x-a)**2))
func=lambda x:(2000*x[0]+3000*x[1]+4500*x[2])
bnds((1,10000),(1,10000),(1,10000))
res=opt.minimize(fun=func,x0=np.array([2,1,1]),bounds=bnds)
print(res)

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```from  scipy import integrate
from scipy import pi
def f(h):
    return 88.2*pi*(5-h)
v,err=integrate.quant(f,0,5)
print(v)