kx_engineer_productivity.py

import numpy
import scipy.optimize
from matplotlib import pyplot

cs = numpy.linspace(0.01, 0.99, 100)
ks = []

for c in cs:
    def f(log_k):
        k = numpy.exp(log_k)
        return (c/k + 1-c)*k**0.6

    res = scipy.optimize.minimize(f, 0)
    optimal_log_k, = res.x
    ks.append(numpy.exp(optimal_log_k))

pyplot.semilogy(cs, ks)
pyplot.grid()
pyplot.xlabel('Fraction of the time spend on real work')
pyplot.ylabel('What multiple engineers should you hire')
pyplot.savefig('2x-engineer-productivity.png')