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.
This exercise is part of the course
Introduction to Optimization in Python
Exercise instructions
- 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.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# 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}")