# Case analysis Red brand canners

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MODEL DESCRIPTION
The problem: Mr Mitchell Gordon, vice president of operations of Red Brand Canners, wants to determine the amount of tomato products to pack that season based on the demand for the coming year. A total of 3 million pounds of tomato crop was purchased, however, according to Dan Tucker, the production manager, about 20% of the tomato crop was grade A quality and the remaining portion was grade B. In addition, although the company has ample production capacity, the production manager alerted that it was impossible to produce all whole tomatoes because only a small portion of the crop was grade A quality. The demand per cases, the contribution per product (Canned whole tomatoes, Tomato juice and Tomato paste) and quality results were given to us for the analysis and are detailed on Appendix A. You want to determine the optimal canning policy for the season’s crop.

The solution approach: Using a mathematical model and linear programming we obtained the proposed solutions. The main objective of this model is to determine the optimal canning policy for the season’s crop and maximize profits. The mathematical model consists of an objective function, 6 variables and 7 constraints based on the information provided to us. The detailed mathematical model is on appendix B. The optimal solution was obtained from Excel Solver by the simplex linear programming method.

Variables: The mathematical model has in total 6 nonnegative variables defined in terms of pounds of tomatoes. Each product has 2 variables, one representing the pounds of grade A tomatoes and the other representing the pounds of grade B tomatoes.

Constraints: Seven (7) constraints related to limitations on the demand, quality and quantity of the pounds of tomatoes for the products. The demand forecast constitutes three constraints, one for each type of product based on the information provided. In terms of quality, we determined two constraints, one for canned whole tomatoes and one for

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