Product Mix Case

Executive Report

A. Background

TJ’s Inc., makes three nut mixes which are sold to grocery chains throughout the Southeast region of the country. The three mixes are referred to as the Regular Mix, Deluxe Mix, and the Holiday Mix. They are all made with 5 different types of nuts ( Almond, Brazil, Filbert, Pecan, Walnut). Tj’s has high demand during the fall season and already has large orders placed. TJ’s is committed to using the available nuts to maximize profit, and any nuts not used will be given to a local charity. Even if it is not profitable to do so, TJ’s president indicated that all orders currently received must be satisfied.

B. Objective

Determine how many pounds of each product mix should be produced so that profits will be maximized for the fall season. We assume that the nuts are perishable and cannot be used beyond this season.

C. Methodology

A Linear Mathematical Program was created.

The Program was solved by using Excel Solver.

D. Results

The Objective Function Value originally showed profit of $61375, but the sunk cost of shipping all the nuts of $36450 needed to be subtracted. The optimal solution to the problem will provide a maximum profit of $24925. The optimal values of the decision variables are given by R = 17500, D = 10625, and H = 5000. The optimal decision for TJ’s is to produce 17500 pounds of the Regular Mix, 10625 pounds of the Deluxe Mix, and 5000 pounds of the Holiday Mix.

item | R | D | H | total |

reg mix | 1 | | | 10000 |

deluxe mix | | 1 | | 3000 |

holiday mix | | | 1 | 5000 |

almonds | 0.15 | 0.2 | 0.25 | 6000 |

brazil | 0.25 | 0.2 | 0.15 | 7500 |

filberts | 0.25 | 0.2 | 0.15 | 7500 |

pecan | 0.25 | 0.2 | 0.2 | 7500 |

walnut | 0.1 | 0.2 | 0.25 | 6000 |

| | | | |

| 1.65 | 2 | 2.25 | -36450 |

| | | | |

| Decision Varibles | | |

How much to Produce | 17500 | 10625 | 5000 | |

| | | | |

Max total Profit |...