TJ Nut Inc

TJ Nut Inc. Example
TJ Nut 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 sold as one pound bags which are made by mixing different percentages of five types
of nuts. The Regular Mix consists of 15% almonds, 25% Brazils, 25% filberts, 10%
pecans and 25% walnuts. The Deluxe Mix consists of 20% of each nut type and the
Holiday Mix consists of 25% almonds, 15% Brazils, 15% filberts, 25% pecans and 20%
TJ’s accountant has analyzed the cost of production (excluding the cost of the 5 types of
nuts) and the sales price per bag. He has determined that the profit contribution per bag
is $1.65 less the cost of nuts for the Regular Mix, $2.00 less the cost of nuts for the
Deluxe Mix and $2.25 less the cost of nuts for the Holiday Mix. TJ’s current inventory
of all the nuts types is 0. TJ has placed an order for a shipment that is due to arrive in a
few days though. This order is for 6000 pounds of almonds at a cost of $7500, 7500
pounds of brazils at a cost of $7125, 7500 pounds of filberts at a cost of $6750, 6000
pounds of pecans at a cost of $7200 and 7500 pounds of walnuts at a cost $7875.
TJ’s has already accepted customer orders for 10,000 bags of Regular Mix, 3,000 bags of
Deluxe Mix and 5,000 bags of Holiday Mix. Because demand is running high, TJ
expects that they will receive many more orders than can be satisfied with their incoming
supply of nuts. As it stands right now, TJ is limited to using the current supply of nuts to
maximize profits for the fall season. TJ would like to determine the optimal product mix
for the three types of nut mixes and the resulting total profit.