Problem 2776. Rule of mixtures (composites) - lower and upper bounds

The rule of mixtures is used in the mechanical design of composite structures to estimate the elastic modulus (Ec) based on the following properties:

    Ef: elastic modulus of the fiber material
    Em: elastic modulus of the matrix material
    ff or fm: volume fraction of the fiber or matrix material (ff = 1 – fm)

Based on these values, the lower-bound estimate of elastic modulus is calculated by:

Ec = 1 / (ff / Ef + (1 – ff) / Em).

On the other hand, the upper-bound (linear) estimate of elastic modulus is calculated by:

Ec = ff * Ef + (1 – ff) * Em.

Write a function to calculate both bounds for various values. Also, return the difference between the modulus estimates and the ratios of this difference to both moduli estimates.