# Group 2 Red Brand Canners Case Study

Topics: Tomato, Optimization, Tomato sauce Pages: 14 (2910 words) Published: March 29, 2015
Optimal Solutions
Carleton University
29 Jan 2015

Mr. Mitchell Gordon,
Vice president of operations
Red Brand Canners.
Dear Mr. Gordon,
We have completed the analysis of your goal to determine the amount of tomato products to pack for the season. This report consists of defining the whole problem and the solution as you desired to be, with respect to limitations and possibilities that already exist, management policies, recommendations and alternatives. By modulating the problem, we found out that the highest profit is obtained with 615.000 pounds of canned whole tomatoes from grade A and 205,000 from grade B, 65.000 juice from grade A and 195.000 from B, and 2.000.000 paste tomatoes from grade B. So the whole net profit will be \$47.600. This means that by adding 80.000 pounds of grade A tomato, the achievement for the whole profit will stand at it is optimal region. Furthermore, the report provides information about diverse alternatives such as what happens if the amount of any products are increased, or which type of quality would be better to use for juice or any other products, cost changes and how they influences the whole objective function.

The attached report gives the details of what we have done in order to come up with the best solution, the analysis procedure, the recommendations and the alternatives that can be considered in the problem. If you have any question or require further information, please do not hesitate to contact us.

Sincerely,
Jennifer Solano
Nima Molajafar
Wenhao Ma

RED BRAND CANNERS

By
Jenniffer Solano
Nima Molajafar
Wenhao Ma

TOMS 5301 – Modeling Business Decisions
Prof. Uma Kumar
January 29th 2015

SUMMARY
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. Optimal Solutions was hired to make recommendations and provide the best production distribution for the company.

The solution. Based on mathematical models and linear programming we obtained the optimal solution that has the best canning policy for the season’s crop and also maximize profits. The optimal solution was obtained when we added 80.000 pounds   of

tomato

crop
to
the
initial
model.
The best distribution of the tomato products to pack and the maximum profit with this combination is summarized in the following table:

Canned
Whole

tomatoes

Tomato
juice

Tomato
paste

A

B

A

B

A

B

#
of
pounds

615.000

205.000

65.000

195.000

0

2.000.000

Net
Profit

\$47.600

Recommendation
and
conclusion.
Taking
into
account
the
results,
we
recommend

you
to
increase
the
amount
of
tomato
crop
to
3.080.000
pounds
because
the
extra

80.000
pounds
will
help
to
increase
the
total
profit
by
\$0.09
per
pound,
which

means
80.000
x
\$0.09
=
\$7200.
However,
it
is
important
to
take
into
account
that

even
if
the
company
more
than
80.000
pounds
up
to
600.000
pounds,
it
will

continue
increasing
the
profits.
If
your
company
our
recommendation,
the

net
profit
will
increase
and
the
production
will
be
optimum.

INITIAL ANALYSIS
After our initial meeting, where we received your requirements and understood the currently situation of your company, in addition you asked us to find out how the limitation for whole tomato production was determined based   on...