Summary of the Problem: TJ’s, Inc. , makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred as the Regular Mix, Deluxe Mix, Holiday Mix. Now TJ’s is committed to using the available nuts to maximize profit of the fall seasons, and they must satisfy the received orders. Problem Solving Approach: This problem was solved using Excel Solver LP Programming. The decision variables are pounds of each type of Mix. The objective function was a formula of profit contribution for each Mix.
The constraints are the nuts purchased the following shipment and the orders that need to be satisfied. The following summarizes the variables and coefficients of the mathematical model: Variable or CoefficientUnit of MeasureDescription RPoundsPounds of Regular Mix DPoundsPounds of Deluxe Mix HPoundsPounds of Holiday Mix DescriptionRegularDeluxe HolidayShipment amountCost per shipment Orders (Pounds)1000030005000 Almond Consist percentage0. 15 0. 20 0. 25 60007500 Brazil Consist percentage0. 5 0. 20 0. 15 75007125 Filbert Consist percentage0. 25 0. 20 0. 15 75006750 Pecan Consist percentage0. 10 0. 20 0. 25 60007200 Walnut Consist percentage0. 25 0. 20 0. 20 75007875 Profit (Dollars) ( Not include cost of nuts) 1. 6522. 25 The following is the mathematical formulation of the problem: Maximize1. 65R+2D+2. 25HObjective function Subject to: 0. 15R+0. 2D+0. 25H= 10000 Deluxe 10625>= 3000 Holiday5000>= 5000 Constrains2Nuts Used Available Almond6000