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.
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Grade B tomatoes were averaged 5 points per pound. The minimum average input quality for canned whole tomatoes was 8 points per pound and for tomato juice was 6 points per pound.
• The whole tomato production was limited to 800.000
Variables: The following variables were defined to do the calculations and will be used for our analysis.
X1 è pounds of grade A tomatoes in canned whole tomatoes. X2 è pounds of grade B tomatoes in canned whole tomatoes.
9X1 + 5X2 ≥ 8 (X1 + X2) è 9X1 + 5X2 = 8 (X1 + X2) è 9X1 – 8X1 = 8X2 -‐ 5X2 è X1 = 3X2
We know that X1 is maximum 600.000 pounds of the total crop. Substituting this •
•
•
value on the equation above we obtained the value for X2: !"".!!!
X1 = 3X2 è 600.000 = 3X2 è X2 = ! = 200.000
Adding the two values of X1 and X2 we obtained the limited production amount for whole tomatoes:
X1 + X2 =
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Aramyan, L. H., Meuwissen, M. M., Oude Lansink, A. M., van der Vorst, J. J., van Kooten, O., & van der Lans, I. A. (2009). The perceived impacts of quality assurance systems on tomato supply chain performance. Total Quality Management & Business Excellence, 20(6), 633-653.
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