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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.

Este ejercicio forma parte del curso

Introduction to Optimization in Python

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Instrucciones del ejercicio

  • Create a sympy symbol, q, that represents the quantity of bicycles produced.
  • Find the derivative of the objective function c with respect to q, dc_dq, using sympy.
  • Solve the derivative to find the optimum price.

Ejercicio interactivo práctico

Prueba este ejercicio completando el código de muestra.

# 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}")
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