Consider the production planning problem discussed in Example $2\mathrm{.}14$

$($Section $2\mathrm{.}17).$ Assume now that $$backorders$$ are allowed, that is$,$ if

we do not have sufficient stock, we can backorder so that the order can

be supplied in a later week. However, this incurs a backorder penalty

cost of $$4$ per unit per week