Diamant Foods Company

Diamant Foods Company produces a variety of food products, including a line of candies. One of its most popular candy items is Divine Diamonds, a bag of a dozen individually wrapped diamond$-$ shaped candies made primarily from a blend of dark and milk chocolates, macademia nuts, and a blend of heavy cream fillings. The item is relatively expensive, so Diamant Foods produces it only for its eastern market, encompassing urban areas such as New York, Atlanta, Philadelphia, and Boston. The item is not sold in grocery or discount stores but mainly in specialty shops and specialty groceries, candy stores, and department stores. Diamant Foods supplies the candy to a single food distributor, which has several warehouses on the East Coast. The candy is shipped in cases of $60$ bags of the candy per case. Diamonds sell well, despite the fact that they are expensive, at $$9\mathrm{.}85$ per bag $($wholesale$).$ Diamant uses high quality, fresh ingredients and does not store large stocks of the candy in inventory for very long periods of time.

Diamant$$s distributor believes that demand for the candy follows a seasonal pattern. It has collected demand data $($i$.$e$.$ cases sold$)$ for Diamonds from its warehouses and the stores it supplies for the past $3$ years, as follows:$$Month

January February March April

May

June

July August September October November December

Year $1$

$192$

$210$

$205$

$260$

$228$

$172$

$160$

$147$

$256$

$342$

$251$

$273$

Demand $($cases$)$ Year $2$

$212$

$223$

$216$

$252$

$235$

$220$

$209$

$231$

$263$

$370$

$260$

$277$

Year $3$

$228$

$231$

$226$

$293$

$246$

$229$

$217$

$226$

$302$

$411$

$279$

$293$The distributor must hold the candy inventory in climate$-$controlled

handling it$.$ The annual carrying cost is $$116$ per case. Diamonds must be shipped a long distance from the manufacturer to the distributor, and in order to keep the candy as fresh as possible, trucks must be air$-$conditioned, shipments must be direct and shipments are often less than a truckload. As a result, the ordering cost is $$4,700.$

Diamand Foods makes Diamonds from three primary ingredients it orders from different suppliers: dark and milk chocolate, macadamia nuts, and a special heavy cream filling. Except for its unique shape a Diamond is almost like a chocolate truffle. Each Diamond weighs $1\mathrm{.}2$ ounces and requires $0\mathrm{.}70$ ounce of blended chocolates, $0\mathrm{.}50$ ounce of macadamia nuts, and $0\mathrm{.}40$ ounce of filing to produce $($including spillage and waste$).$ Diamant Foods orders chocolate, nuts, and filing from its suppliers by the pound. The ordering cost is $$5,700$ for chocolate, and the annual carrying cost is $$0\mathrm{.}45$ per pound. The ordering cost for macadamia nuts is $$6,300,$ and the annual carrying cost is $$0\mathrm{.}63$ per pound. The ordering cost for filling is $$4,500,$ and the annual carrying cost is $$0\mathrm{.}55$ per pound.

Each of the suppliers offers the candy manufacturer a quantity discount price schedule for the ingredients, as follows:

warehouses and be careful in$$Chocolate

Quantity $($lb$)$

$050,00050,001100,000100,001150,000$

$150\mathrm{.}001+$

Macadamia Nuts

Filling

Quantity $($lb$)$

$040,00040,00180,000$

$80,001+$