This case study involves the production of two types of wine by a local vintner with the purpose of selling it to the local shop. He knows the profit ($/gal) for both types, i.e., medium white ( M ) and dry white ( D ). Production of the wine requires a combination of grapes, sugar and extract. The exact requirements are known for both M and D . The constraints for this problem are given by the limitations for grapes, sugar and extract. Obviously, the objective here is that the vintner should maximize his profit in selling to the local shop. Clearly, there is sufficient information to formulate in mathematical form a linear programming problem. This L.P. problem is solved using the simplex method. Also, sensitivity analysis is employed to examine the effects of changes in the parameters on the optimal solution. The solution is validated by using LINDO and MAPLE. 2. Problem Statement A local wine producer makes two types of wine, medium white (M ) and dry white ( D ), to sell to the local shop. He makes $5 profit per gallon from M and $4 a gallon from D . Now M requires 3 boxes of grapes, 4 lb of sugar and 2 pints of extract per gallon. Also, D requires 4 boxes of grapes, 2 lb of sugar and 1 pint of extract per gallon. The vintner has 14 boxes of grapes, 8 lb of sugar and 6 pints of extract left before selling his business. We wish to decide how to use these resources to maximize profit. (a) We will create and solve the dual linear programming problem. Then we will find the optimal solution to the primal problem by interpreting the optimal dual tableau. (b) By performing sensitivity analysis we will determine for what range of profit for dry white wine the present optimal basis remains optimal. (c) Suppose the wine producer wishes to vary the supply of grapes he requires in the production of his two white wines. He wants to know if his wine-making business will still be profitable if for some reason there is a shortage of grapes. We will then determine how much below 14 boxes the supply can drop for the present basis to be still optimal. (d) We return to the original problem but suppose now that the medium white wine requires 1 2 7 units of extract. We will use sensitivity analysis to determine how this affects the solution.