Red Brand Canners

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