Problem $3\mathrm{.}3$

Samsung's mobile communications division, a smartphone manufacturer, uses $20,000$ memory chips per

month. Their trucking company charges Samsung $300$ per shipment, independent of the quantity

purchased. The manufacturer 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, and $0\mathrm{.}92$ per

chip for orders larger than $36,000$ units. Samsung incurs a holding cost of $15$ percent.

$29.$ What is the optimal order quantity for Samsung?

$30.$ What is the annual cost of such a policy?

$31.$ What is the cycle inventory of memory chips at Samsung?

$32.$ How does it compare with the cycle inventory if the manufacturer does not offer a quantity discount but

sells all chips at $1,0\mathrm{.}96$ and $0\mathrm{.}92$ per unit respectively?