Case Problem $1$: Product Mix

TJ$,$ Inc. makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as the Regular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts.

In preparation for the fall season, TJ$,$ Inc. just purchased the following shipments of nuts at the prices shown: See Picture

The Regular Mix consists of $15\%$ almonds, $25\%$ Brazil nuts, $25\%$ filberts, $10\%$ pecans, and $25\%$ walnuts. The Deluxe Mix consists of $20\%$ of each type of nut, and the Holiday Mix consists of $25\%$ almonds, $15\%$ Brazil nuts, $15\%$ filberts, $25\%$ pecans, and $20\%$ walnuts.

An accountant at TJ$,$ Inc. analyzed the cost of packaging materials, sales price per pound, and so forth, and determined that the profit contribution per pound is $$1\mathrm{.}65$ for the Regular Mix, $$2\mathrm{.}00$ for the Deluxe Mix, and $$2\mathrm{.}25$ for the Holiday Mix. These figures do not include the cost of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets.

Customer orders already received are summarized here: See Picture The Regular Mix consists of $15\%$ almonds, $25\%$ Brazil nuts, $25\%$ filberts, $10\%$ pecans, and

$25\%$ walnuts. The Deluxe Mix consists of $20\%$ of each type of nut, and the Holiday Mix

consists of $25\%$ almonds, $15\%$ Brazil nuts, $15\%$ filberts, $25\%$ pecans, and $20\%$ walnuts.

An accountant at TJ$,$ Inc. analyzed the cost of packaging materials, sales price per

pound, and so forth, and determined that the profit contribution per pound is $$1\mathrm{.}65$ for the

Regular Mix, $$2\mathrm{.}00$ for the Deluxe Mix, and $$2\mathrm{.}25$ for the Holiday Mix. These figures do

not include the cost of specific types of nuts in the different mixes because that cost can

vary greatly in the commodity markets.

Customer orders already received are summarized here:

Because demand is running high, it is expected that TJ$,$ Inc. will receive many more orders than can be satisfied.

TJ$,$ Inc. is committed to using the available nuts to maximize profit over the fall season; nuts not used will be given to a local charity. Even if it is not profitable to do so$,$ TJ$,$ Inc.$$s president indicated that the orders already received must be satisfied. LO $2,3,5,8$

Managerial Report

Perform an analysis of the TJ$,$ Inc.$$s product$-$mix problem, and prepare a report for the pres$-$ ident of TJ$,$ Inc. that summarizes your findings. Be sure to include information and analysis on the following:

$1.$ The cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes

$2.$ The optimal product mix and the total profit contribution

$3.$ Recommendations regarding how the total profit contribution can be increased if

additional quantities of nuts can be purchased

$4.$ ArecommendationastowhetherTJ,Inc.shouldpurchaseanadditional$1000$pounds

of almonds for $$1000$ from a supplier who overbought

$5.$ Recommendations on how profit contribution could be increased $($if at all$)$ if TJ$,$ Inc.

does not satisfy all existing orders