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
 

Grade
 
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
  buys
  more
  than
  80.000
  pounds
  up
  to
  600.000
  pounds,
  it
  will
 
continue
  increasing
  the
  profits.
  If
  your
  company
  adopts
  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...
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