A customer requires $50,65,100,$ and $70$ units of a commodily during the naxt $4$ months, respectively, and no bacldogging is allowed; that is$,$ the customer's requirementen time the mel on time. Production costs $$5,$$$8,$$$4,$ and $ per unit during these months. The storage cost trom one month to the nath is $$2$ par unit $($assassed on ending inventory$).$ It is estimated that each unit on hand at the end of month $4$ could be sold for $$6.$

$($A$)$ Determine how to minimire the net cost incurred in meeting the demands for the next four months.

$($B$)$ Starting with the optimal solution to $($A$),$ use Solver Table sadin to see whal hacgens to the foctelen varlables the total cost when the initial inventiory varies from $0($the implied wabe in $($A$)$ to $100$ in $10-$units increments. How much lower would the fotal cost be if the compary starled with $10$ units in inventory, rather than noria? Would the same cost decrease ocour for every $10-4$ in increase in inflial hrepacy?