Soru

A shipping company offers two types of delivery services: standard and express. The total shipping cost, in dollars, for a package sent via standard service is modeled by the function $C(w) = 1.25w + b_s$, where $w$ is the weight of the package, in pounds, and $b_s$ is a constant representing the flat handling fee. The total shipping cost, in dollars, for a package sent via express service is modeled by the function $E(k) = m_e k + b_e$, where $k$ is the weight of the package, in kilograms, and $b_e$ is a constant representing the flat handling fee.

The rate of change of the express shipping cost with respect to the package's weight, in dollars per kilogram, is $2.4$ times the rate of change of the standard shipping cost with respect to the package's weight, in dollars per pound. The flat handling fee for the express service is $4.50$ dollars more than the flat handling fee for the standard service. If it costs $58.50$ dollars to ship a package weighing $26.4$ pounds using the express service, what is the cost, in dollars, to ship a package weighing $20$ pounds using the standard service? (Assume $1\text{ kilogram} = 2.2\text{ pounds}$.)