Sunk -versus- Variable Costs Only the variable costs are relevant in optimization models. Sunk costs do not need to be added as a separate term in the objective. The problem can be optimized without it and the sunk cost subtracted later. Sunk costs should never be allocated across the coefficients of the decision variables. This will influence the values identified for the decision variables and result in inappropriate allocations.

TJ Inc. Product Mix Problem Three nut products: regular, deluxe and holiday mixes Each mix consists of different proportions of five nuts: almonds, brazils, filberts, pecans and walnuts Management wants an analysis and recommendation for the product mix problem

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

Constraints Limited supply of each type of nut Existing customer orders that must be satisfied Demand is greater than capacity

Profit contribution & costs Profit contribution which includes relevant variable costs are $1.65/lb for regular, $2.00/lb for deluxe, and $2.25 for holiday. Cost per pound of the nuts included in each mix are $ for regular, $1.07 for deluxe, and $1.10 for holiday. These costs are sunk however and should not be included in the product mix decision.

LP Formulation maximize 1.65 X1+ 2 X X3 subject to.15X1+.2X2+.25X3<=6000 almond lbs.25X1+.2X2+.25X3<=7500 brazil lbs.25X1+.2X2+.15X3<=7500 filbert lbs.10X1+.2X2+.25X3<=6000 pecan lbs.25X1+.2X2+.20X3<=7500 walnut lbs X1 >=10000 lbs X2 >=3000 lbs X3>=5000 lbs

Optimal Product Mix Produce 17,500 lbs of regular mix, 10,625 lbs of deluxe mix and 5000 lbs of holiday mix. Resulting total profit is $24,925 ($61,375 less the $36,450 sunk cost of the nuts)