Present the cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes. Discuss the optimal product mix and the total profit contribution. Give recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can be purchased. Give a recommendation as to whether TJ’s should purchase an additional 1000 pounds of almonds for $1000 from a supplier who overbought. Give recommendations on how profit contribution could be increased (if at all) if TJ’s does not satisfy all existing orders.
The cost per pound of the almonds is $1. 25 The cost per pound of the Brazil Nuts is $. 95. The cost per pound of the filberts is $. 90. The cost per pound of the pecans is $1. 20. Finally the cost per pound of the walnuts is $1. 05. Therefore, the cost per pound of the Regular Mix is $1. 03, of the Deluxe Mix is $1. 07, of the Holiday Mix is $1. 10 2. The optimal product mix is to produce 17500 pounds of the Regular Mix, 10625 pounds of the Deluxe Mix, and 5000 pounds of the Holiday Mix. The total profit contribution after subtracting the total cost per shipment of the various nuts in the mixes is $24925.
The recommendation to the question “if an additional amount of nuts can be purchased to increase the profit contribution” would be to purchase more almonds and walnuts. By looking at the constraint for the dual prices for almonds you will see for every one pound increase in almonds used, the objective function/profit contribution will increase at a rate of $8. 50. And by looking at the dual prices for walnuts you will see for every one pound increase in walnuts used, the objective function/profit contribution will increase at a rate of $1.
If an additional 1000 pounds of almonds were offered at a price of $1000 from a suppler that overbought, we would recommend TJ’s to purchase the almonds. The reason we recommend this is because TJ’s would be purchasing the almonds at a price of $1. 00 per pound, decreasing their cost by twenty-five cents per pound. Also they would increase their available pounds of almonds from 6000 to 7000, therefore increasing their profit to $29,883. 33 giving them an increase of $4,958. 33. 5.
If TJ’s is not able to satisfy all existing orders, the recommendation we would give would be to increase the purchase of nuts for all of the mixes. By doing this they could reach an optimal solution to the objective function of 1. 65R + 2. 00D + 2. 25H – 36450 that would maximize the profit contribution. Also we would recommend to TJ’s not to fill all orders for the Holiday Mix. Conclusion To maximize TJ’s profit over the fall season, we used a linear programming model to decide how many pounds of Regular Mix, Deluxe Mix, and Holiday Mix they should produce.
We declared the decision variables as follows to be R stands for pounds of Regular Mix, D stands for pounds of Deluxe Mix, and H stands for pounds of Holiday Mix. We discovered the objective function is 1. 65R + 2. 00D + 2. 25H + 36450. After plugging in the constraints with this information we discovered that the pounds produced should be 17500 of Regular Mix, 10625 of Deluxe Mix, and 5000 of Holiday Mix. Other suggestions were to purchase more almonds and walnuts and to reduce the pounds of Holiday Mix produced.