In Section $7\mathrm{.}2$ we introduced a model for determining $$ which is the number of

persons receiving a first vaccine dose in period p $,$ p $=1,...,$ P$,$ where P is the number of periods

in the planning horizon. The objective was to determine the values of $$ so as to maximize

vaccinated person$-$periods, or days, if a period is a day in length. Mathematically, the goal was to

maximize $$

$=1$ Vp $($ P $$ p $+1)$

subject to constraints expressed in equation $(7\mathrm{.}1).$ We also showed that this linear program could

be formulated as follows.

Define $$ to be the on$-$hand vaccine supply at the end of period p$.$ Then the optimization problem