include lingo codes Solution to problemSolution to problem 4, 52,3Optimal Objective ValueOptimal Objective Value66333.33361375VariableValue Reduced CostVariableValueReduced CostR1750011666.6667D10825D17916.6667so005000DescriptionSlackSlackConstraintDual ValueConstraintDual ValueSurplusSurplusAlmonds8.51416.66667Brazil2250250Filberts3250250Pecans487545.66667Walnuts1.54.33333Regular750061666.66667Deluxe7762514916.66667Holiday-0.175-0.03333Objective AllowableAllowableObjectiveAllowableAllowableCoefficientIncreaseDecreaseCoefficient IncreaseDecrease1.650.350.151.650.10.652020.107691.30.023532.250.175Infinite2.250.03333InfiniteRHSAllowableAllowableRHSAllowableAllowableValueIncreaseDecreaseValueIncreaseDecrease6000 583.333336107000Infinite416.666677500Infinite2507500Infinite2507500Infinite2507500Infinite2506000Infinite8756000250179075001000025075075002502507500Infinite10000 1666.66667Infinite30007625Infinite3000 14916.6666Infinite5000so005000 10529.411750004692 3 Problem: PRODUCT MIXTJs,Inc, makes three nut mixes for sale to grocery chains located in the Southeast. The three mixes, referred to as theRegular Mix, the Deluxe Mix, and the Holiday Mix, are made by mixing different percentages of five types of nuts. Inpreparation for the fall season, TJ's has just purchased the following shipments of nuts at the prices shown:Shipment Amount (pounds)Type of NutCost per Shipment (S)Almond60007500Brazil75007125Filbert75006750Pecan60007200Walnut75007875The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts. The DeluxeMix 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. TJ's accountant analyzed the cost of packaging materials, sales price per pound, and soforth, 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. These figures do not include the cost of specific types of nuts in the different mixesbecause that cost can vary greatly in the commodity markets. Customer orders already received are summarized here:Type of Mix Orders (pounds)RegularDeluxeHoliday10,0003,0005,000Because demand is running high, it is expected that TJ's will receive many more orders than can be satisfied. TJ's iscommitted to using the available nuts to maximize profit over the fall season; nuts not used will be given to a localcharity. Even if it is not profitable to do so, TJ's president indicated that the orders already received must be satisfied.Managerial ReportPerform an analysis of TJ's product-mix problem, and prepare a report for TJ's president that summarizes yourfindings. Be sure to include information and analysis on the following:1. The cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes.2. The optimal product mix and the total profit contribution.3. Recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can bepurchased.4. A recommendation as to whether TJ's should purchase an additional 1000 pounds of almonds for $1000 from asupplier who overbought.5. Recommendations on how profit contribution could be increased (if at all) if TJ's does not satisfy all existingorders.

Product Mix - It is mix of a group of the company sells every type of product using available…

Problem: PRODU TJ's, 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 made by mixing different percentages of five types of nuts. In preparation for the fall season, TJ's has just purchased the following shipments of nuts at the prices shown: Shipment Amount (pounds) Type of Nut Cost per Shipment (S) Almond 6000 7500 Brazil 7500 7125 Filbert 7500 6750 Pecan 6000 7200 7875 Walnut The Regular Mix consists of 15% almonds, 25% Brazil nuts, 25% filberts, 10% pecans, and 25% walnuts. The Deluxe 7500 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. TJ's accountant 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. These figures do not include the cost of specific types of nuts in the different mixes because that cost can vary greatly in the commodity markets. Customer orders already received are summarized here: Type of Mix Orders (pounds) 10,000 3,000 5,000 Regular Deluxe Holiday Because demand is running high, it is expected that TJ's will receive many more orders than can be satisfied. TJ's 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's president indicated that the orders already received must be satisfied. Managerial Report Perform an analysis of TI's product-mix problem, and prepare a report for TJ's president that summarizes your findings. Be sure to include information and analysis on the following: 1. The cost per pound of the nuts included in the Regular, Deluxe, and Holiday mixes. 2. The optimal product mix and the total profit contribution. 3. Recommendations regarding how the total profit contribution can be increased if additional quantities of nuts can be purchased. 4. A recommendation as to whether TJ's should purchase an additional 1000 pounds of almonds for $1000 from a supplier who overbought. S. Recommendations on how profit contribution could be increased (if at all) if T's does not satisfy all existing orders.