Design a pavement for a rural interstate highway. The expected design ESAL is $13$x$106.$ The pavement structure is to consist of asphalt concrete with an elastic modulus of $400000$psi, a granular base with an elastic modulus of $26000$psi, and a granular subbase with an elastic modulus of $12000$psi. The elastic modulus of the subgrade is $8000$psi. It is estimated that it will take a week for water to drain from the pavement and that the pavement will be saturated about $15\%$ of the time. Assume that a reliability level of about $90\%$ is required and that the initial serviceability index is $4\mathrm{.}2$ and the final serviceability index is $2\mathrm{.}5.$