TJ Inc.’s makes three nut mixes for sale to grocery chains located in the Southe
ID: 3262702 • Letter: T
Question
TJ Inc.’s 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.’s just purchased the following shipments of nuts as shown:
Type of Nut |Shipment Amount (pounds)
Almond | 6000
Brazil | 7500
Filbert | 7500
Pecan | 6000
Walnut | 7500
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 $1.65 for the Regular Mix, $2.00 for the Deluxe Mix, and $2.25 for the Holiday Mix. Customer orders already received are summarized here:
Type of Mix | Orders (pounds)
Regular | 10,000
Deluxe | 3,000
Holiday | 5,000
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. Perform an analysis of the TJ Inc.’s product-mix problem, and prepare a report for the president of TJ, Inc. that summarizes your findings. Be sure to include information and analysis on the following:
1. The optimal product mix and the total profit contribution;
2. A recommendation as to whether TJ, Inc. should purchase additional quantities of Brazil nuts;
3. A recommendation as to whether TJ, Inc. should purchase an additional 1000 pounds of almonds for $1000 from a supplier who overbought.
Use Excel and show ALL WORK
Explanation / Answer
Solution:
1) The analysis was done using Excel with the following LP model:
2) Currently there is an extreme over-supply of all types of nuts, and
for that reason the problem was constrained by the number of orders
placed. At this point no particular type of nut is preventing a higher
profit contribution. In fact, if we were to remove the constraints
relating to the number of orders received, the profit contribution
would skyrocket to $62250, and at that point we can see that pecans
would be the only type with excess 'slack' (given the current mixes).
3) The correct solution to this question can really only be found by
plugging in the change into the model. The first thing to note is that
you are able to obtain these almonds cheaper that before ($0.25/lb
discount). In addition, if no constraints are placed on order levels,
we find that the profit contribution rises from $62250 (as we saw from
the previous question) to $66500. This is a marginal profit of $4250,
and when you offset the $1000 cost for the almonds it is $3250 in pure
profit. Therefore it is recommended that this purchase be made
(assuming orders are anticipated to consume the increased availability
that will result).
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