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Exercise

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.

Instructions

100 XP
  • 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.