$($P$2)$ The question refers to the same model as P$1,$ with $L=2$ weeks required between doses. Suppose

we have new supply projections given in the chart below. Write the LOP to determine the optimal

vaccination schedule, and solve it by specifying number of first doses $v_j$ and amount of vaccine stock

held $N_j,$ for each $j=1,$cdots,$12.$ Also state the value of your vaccination plan in person weeks of

protection. Hint: notice the supply does not increase every $2$ periods.