Mail by Boat: The Dispatch Interval That Balances Waiting Letters Against the Cost of the Trip

For a settlement reached by boat, every dispatch decision trades a trip's cost against a pile of waiting letters. This paper prices both sides: a mail trip costs a stated USD 38, and a letter held one day carries a stated delay cost of USD 0.04. At 160 items a day the balance falls at a dispatch interval of 3.45 days, an average wait of 1.72 days, and a combined daily cost of USD 22.05 — 46.5 percent cheaper than dispatching daily (USD 41.2) and 20.8 percent cheaper than a weekly boat (USD 27.83). The optimal interval follows the square root of volume, so quadrupling the mail only halves the interval; a service standard stated as a maximum wait caps the interval from the other side and binds exactly when volume is low. SIMULATED, NOT MEASURED.