A newsboy sells newspapers and his goal is to maximize profit. He kept a record of his sales for $125$ days with the following result: His ordering policy is to order an amount each day that is equal to the previous day's demand.

A newspaper costs the carrier $50$ cents and he sells it for $$1\mathrm{.}00.$ Unsold papers are returned and he receives $25$ cents $($for a loss of $25$ cents$).$