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 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 unused.

Note also that the “Less allocated OHD”, which is to be considered a fixed cost, was split among products

also considering Tomato Juice that Copper decided not to produce. In this case less allocated OHD should

have been distributed only among the products that would be effectively produced. Cooper made the

same mistake in calculating the fruit