Samsung's mobile communications division uses

$20$

$,$

$000$

$$memory chips per month. Their trucking company charges Samsung $

$300$

$$per shipment, independent of the quantity purchased. The manufacturer of the memory chips offers an all unit quantity discount with a price of $

$1$

$$per memory chip for orders under

$18$

$,$

$000$

$$units$,$ $

$0\mathrm{.}96$

$$per chip for orders between

$18$

$,$

$000$

$$and

$36$

$,$

$000$

$$units

$($

including

$18$

$,$

$000$

$$and excluding

$36$

$,$

$000)$

$,$

$$and $

$0\mathrm{.}92$

$$per chip for orders

$36$

$,$

$000$

$$units and larger. Samsung incurs a holding cost rate of

$15$

$\%$

$$per year. What is the optimal lot size and optimal total cost

$($

TC

$*)$

$$for Samsung?