Question No: $12\mathrm{.}18$

The catering manager of La Vista Hotel, Lisa, is disturbed by the amount of silverware she is losing every week. Late Friday night, when her crew tried to set up for a banquet for $500$ people, they did not have enough knives. She decides she needs to order some silverware, but wants to take advantage of any quantity discounts her vendor will offer.

For a small order $(2,000$ or fewer pieces$),$ her vendor quotes a price of $ $1\mathrm{.}80/$piece$.$

If she orders $2,001-5,000,$ the prices drop to $ $1\mathrm{.}60/$piece$.$

$5,001-10,000$ pieces brings the price to $$1\mathrm{.}40/$piece and $10,001$ and above reduces the price to $ $1\mathrm{.}25.$

DISCOUNT NUMBER

DISCOUNT

QUANTITY DISCOUNT

PRICE $($P$)$

$12,000$ or fewer pieces $ $1\mathrm{.}80/$piece

$22,001-5,000$ $ $1\mathrm{.}60/$piece

$35,001-10,000$ $$1\mathrm{.}40/$piece

$410,001$ and above $ $1\mathrm{.}25$

Information

S order costs$/$ Setup cost $$200$ per order

H annual holding costs $5\%$

D demand $45,000$ pieces

Lisa$$s order costs are $$200$ per order, her annual holding costs are $5\%$ and the demand is $45,000$ pieces. For the best option:

a$.$ What is the optimal order quantity?

b$.$ What are the annual costs of the silverware itself with an optimal order quantity?

c$.$ What is the total cost?