Find the global optimum
You've been provided with the following profit maximization problem and are tasked with finding the global maximum.
\(\Pi= -\frac{1}{4}q^4 + 11q^3 - 160q^2 + 900q\)
\(0\) is a natural lower bound for quantity and you observed that at \(q=30\) profit is negative, so \(30\) is a good candidate for upper bound.
Find the global optimum for this problem.
basinhopping has been imported for you.
This exercise is part of the course
Introduction to Optimization in Python
Exercise instructions
- Define the dictionary
kwargsof keyword arguments, with bounds \(0\) and \(30\). - Run
basinhopping, with the objective as negative ofprofitand the initial guessx0passed to the minimizerkwargs.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
def profit(q):
return -q**4 / 4 + 11 * q**3 - 160 * q**2 + 900 * q
x0 = 0
# Define the keyword arguments for bounds
kwargs = {"bounds": [(____, ____)]}
# Run basinhopping to find the optimal quantity
result = basinhopping(____ q: -profit(q), ____, ____=kwargs)
print(f"{result.message}")
print(f"The maximum according to basinhopping(x0={x0}) is at {result.x[0]:.2f}\n")