Aggregates with an elastic modulus of $E_a=90$GPa are mixed with the cement paste of $\frac{w}{c}=0\mathrm{.}5$ to produce concrete. Provided that the influence of $\frac{w}{c}$ and degree of hydration, $,$ on the porosity of harden cement paste is given by the empirical relation,

$p=1-\frac{0\mathrm{.}68}{\frac{w}{c}+0\mathrm{.}32}$

when $=0\mathrm{.}9,$ plot the upper and lower elastic moduli of concrete as functions of volume fraction of aggregates.