PART II$.$ Problems $(20$ points$)$ SHOW YOUR WORK

Problem $1(10$ points$)$

A firm is operating a fixed inventory system. One product has the following characteristics:

$\backslash$table$[[$Order cost$,$$$35/$order$],[$Unit cost$,$$$\frac{15}{?}$ unit$],[$Holding cost$/$unit$/$year$,\%$ of unit cost$],[$Annual demand,$1800],[$Lead time,$2$ weeks$]]$

a$.$ What is the EOQ $($using the basic EOQ equation$)$

b$.$ If management decides to use order size of $400$ rather than the EOQ, what will be the impact on total cost? $($Calculate$)$

c$.$ If demand is not constant and it has a weekly standard deviation of $12$ units, what is the reorder point for a service level of $90\%?($Assume that there are $50$ working weeks in one year.$)$

d$.1.,$ Calculate average inventory for part a of the problem.

$2.$ Calculate average inventory for part $c$ of the problem.

a$)$

EOQ$=\sqrt[\phantom{2}]{\frac{2D9}{4}}$

$=\sqrt[\phantom{2}]{\frac{2(3515)}{\mathrm{.}20}}$