Red Brand Canners

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Red Brand
Canners
Case Study
Red Brand Canners
2
Summary
Context ............................................................................................................................................................. 3 Purpose of the document ................................................................................................................................. 3 Cooper’s solution .............................................................................................................................................. 4 Myers’ solution ................................................................................................................................................. 4 Our Solution ...................................................................................................................................................... 5 1.1 Demand constraints .......................................................................................................................... 5 1.2 Tomatoes availability constraints ...................................................................................................... 5 1.3 Quality constraints............................................................................................................................ 6 1.4 Non-negativity constraints ................................................................................................................ 6 1.5 Optimal solution ............................................................................................................................... 6 Comparison between the three solutions ......................................................................................................... 7 Whether or not to buy additional tomatoes ..................................................................................................... 7 Appendix A ....................................................................................................................................................... 9 Red Brand Canners

Context 3
Red Brand Canners is a medium-size company canning and distributing a variety of fruit and vegetable products. This year Red Brand Canners bought the 3,000,000 lbs. grower’s tomato production at an average price of 6 cents per pound. Moreover there’s the possibility to buy an additional quantity of 80,000 lbs. of grade “A” tomato at a price of 8.5 cents per pound.

The tomatoes product range consists of:
• Whole tomatoes
• Tomato juice
• Tomato paste
Average quality for grade “A” tomatoes is 9, while average quality for grade “B” tomatoes is 5. Minimum input quality for whole canned tomatoes is 8, while minimum input quality for tomato juice is 6. Tomato paste can be made entirely from grade “B” tomatoes.

Bill Cooper, the controller, and Charles Myers, the sales manager, gave two contrasting solutions on how to allocate the tomatoes for production.
Purpose of the document
In this document we will see:
• A comparison between Cooper’s solution and Myers’s solution • A different solution
• Whether to buy or not an additional quantity of 80,000 lbs. of grade “A” tomatoes Now we introduce some variables that will be used for the rest of the document: Variable Description
QWA Quantity of whole tomatoes grade “A”
QWB Quantity of whole tomatoes grade “B”
QJA Quantity of tomato juice grade “A”
QJB Quantity of tomato juice grade “B”
QPA Quantity of tomato paste grade “A”
QPB Quantity of tomato paste grade “B”
Red Brand Canners
Cooper’s solution 4
Cooper stated that it was impossible to produce all whole tomatoes since grade “A” tomatoes were insufficient. In his calculation Tomato juice is not profitable so the production of this year should be distributed as follows:

Variable Quantity (lbs)
QWA 600,000
QWB 200,000
QJA 0
QJB 0
QPA 0
QPB 2,000,000
Unused quantity 200,000
Total 3,000,000
Note that 200,000 lbs. of grade “B” tomatoes remains...
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