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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.

Questo esercizio fa parte del corso

Introduction to Optimization in Python

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Istruzioni dell'esercizio

  • Define the dictionary kwargs of keyword arguments, with bounds \(0\) and \(30\).
  • Run basinhopping, with the objective as negative of profit and the initial guess x0 passed to the minimizer kwargs.

Esercizio pratico interattivo

Prova a risolvere questo esercizio completando il codice di esempio.

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")
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