$($a$)$ Use a mathematical model to find an optimal SOP. In your solution, consider that backordering is

allowed at a cost of $$7\mathrm{.}5$ per unit per period and the existing warehouse space is limited and can

hold no more than $500$ units at any given time. Summarize your optimal plan in a table and briefly

discuss it$.$

$($b$)$ If you are presented with an option to rent additional warehouse space, would you consider

renting it$?$ Space can be rented on a monthly basis, in blocks of $100$ units for $$200$ per month per

block. If yes, which month$($s$)$ would you rent it$?$ Why? and what kind of impact do you expect

this additional space will make? You are expected to answer this question by using the LP solution

you obtained in part $($a$),$ without having to re$-$solve the model.