Finding the derivative
For some objective functions, the optimum can be found using calculus by finding the derivative of the function. sympy offers a solution to avoid manually calculating these derivatives. Suppose you work in a firm that produces toy bicycles. You have the following objective function to calculate your costs, \(C\), which is dependent on the variable, \(q\), the quantity of bicycles produced:
\(C = 2000 - q^2 + 120q\)
To find the optimum value of \(q\), you'll find the derivative of the cost with respect to the quantity, \(\frac{dC}{dq}\), using sympy.
symbols, diff, and solve have been loaded for you in this and the next exercise.
Questo esercizio fa parte del corso
Introduction to Optimization in Python
Istruzioni dell'esercizio
- Create a
sympysymbol,q, that represents the quantity of bicycles produced. - Find the derivative of the objective function
cwith respect toq,dc_dq, usingsympy. - Solve the derivative to find the optimum price.
Esercizio pratico interattivo
Prova a risolvere questo esercizio completando il codice di esempio.
# Convert q into a symbol
q = ____
c = 2000 - q**2 + 120 * q
# Find the derivative of the objective function
dc_dq = ____
print(f"The derivative is {dc_dq}.")
# Solve the derivative
q_opt = ____
print(f"Optimum quantity: {q_opt}")