Red Brand Canners – Case Study

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Red Brand Canners is a medium sized company that cans and distributes a variety of fruit and vegetable products under private brands in the western states. The company makes three different tomato products including whole tomatoes, tomato juice and tomato paste. They also distribute Choice peach halves, peach nectarine and cooking apple products.

As part of their discussion over the amount of tomato products to pack in a particular season , it was observed that 3 million pounds of tomatoes are available for packing and distributing. This included two kinds of tomatoes ‘Grade A’ which constituted 20% of available crop and ‘Grade B’ being the remaining.

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The linear programming problem is solved using excel solver and attached in Appendix ‘D’.

Also, the problem has been solved using LINGO as depicted below:

MAX = xa1 + xb1 + xa1 -
xa1 + xa2 + xa3 + xa1 > xa2 > xa3 >

0.0822*(xa1 + xb1)+ 0.066*(xa2 + xb2)+ 0.078*( xa3 + xb3)-186800; xa2 +xa3 = 0; xb1 =0;

Maximum Profit: 53764$ xa1: 615000 lbs xb1: 205000 lbs xa2: 65000 lbs xb2: 195000lbs xa3: 0 lbs xb3: 2000000 lbs

The Sensitivity analysis for the formulation has been attached in Appendix ‘E’.

It is evident that the entire grade ‘A’ tomatoes is used. The shadow price for the slack variable in supply constraint for grade A tomato is 0.0903. Each additional pound of grade ‘A’ tomatoes costing
8.5 cents will increase profits by 0.093 - 0.0850 = 0.0053. Sensitivity analysis also shows that up to an additional 600,000 pounds of grade ‘A’ tomatoes could be purchased without affecting the solution basis.


Based on the above analysis we suggest that the solution provided by Coopers and Myers are inconsistent. The Optimal Solution provided by us gives a profit of $53340 and includes a consistent mix of Grade A and Grade B tomatoes in all the tomato based products.

We also suggest that Red Canners should go ahead and purchase the additional 80,000 pounds
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