Problem 2779. Rule of mixtures (composites) - weighted bound

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 the weighted Ec between both bounds, based on the provided weighting (wt) of the upper bound. (The lower bound will have the remainder of the weighting, or 1–wt.)