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# Red Brand Canners

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## Eugene Sandona

on 20 June 2013

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#### Transcript of Red Brand Canners

RED BRAND CANNERS 600,000 lbs
Grade "B" 3,000,000 lbs of tomatoes at \$0.06 per lb. 80,000 lbs
Grade "A" Tomato Paste Tomato Juice Whole Tomato @ \$0.085 per lb. Ratio of 3:1 \$1.48 per case 18 lbs per case Demand of 800,000 cases Ratio of 1:3 \$1.32 per case 20 lbs per case Demand of 50,000 cases Can use either grade \$1.85 per case 25 lbs per case Demand of 80,000 cases Key Figures:
Maximum of 600,000 lbs. Grade A (+80,000 purchasable)
3:1 ratio for Whole
1:3 ratio for Juice
Market demand of
800,000 cases for Whole
50,000 cases for Juice
80,000 cases for Paste Goal:
Maximize contribution from the sale of the three products Red Brand Canners In 1960’s company canning and distributing variety of fruit and vegetable products under private brands RED BRAND CANNERS Tomato Paste Tomato Juice Whole Tomato 20% Grade "A" 80% Grade "B" The tomatoes were used in production of 3 types of products. Presented by the Controller, Bill Cooper
Produce whole tomatoes
Based on the contribution he calculated for each product using the new accounting method Proposed by the Sales Manager, Charles Myers
Use 2,000,000lbs grade B tomatoes for tomato paste
All of 600,000lbs grade A and the remaining 400,000 grade B tomatoes for juice
No production of whole tomatoes.
Based on marginal profit per product where he calculates the cost of tomatoes according to quality and Solution: Use Linear Programming to find the best outcome! Variables: Objective Function: First to define the variables. Then to calculate the contribution for each product. Problems with alternative 1:

Total production of tomatoes would be limited because:
Production of whole tomatoes is limited to using a proportion of 4 grade A tomatoes for every 1 grade B tomato in order to keep minimum grade quality, therefore limiting the total production to approx. 44,444 cases (800,000lbs/18 lbs per case)
If additional 80,000lbs of grade A tomatoes, is purchased we would still only be able to use the additional 20,000lbs of grade B tomatoes in order to produce whole tomatoes at minimum grade quality Constraints: Are the same as the Key Figures from earlier. At least 180,000lbs of grade B tomatoes left over
(or produce more paste than demand)

After using up all of grade A tomatoes we are not able to produce any juice. The demand for tomato paste is 80,000 cases which would allow the company to use 2,000,000lbs of grade B tomatoes (80,000cases*25lbs per case) potentially leaving 180,000lbs grade B tomatoes unused altogether(2,400,000lbs of grade B – 220,000lbs used for whole tomatoes – 2,000,000lbs used for paste) Using the cost of fruit as a variable cost when it’s in fact sunk cost already incurred

In addition to that, he is using the average cost of fruit, \$0.06 per pound for both grade A and grade B tomatoes without the consideration for quality of each

If we take the cost of fruit out and recalculate variable cost for each product we get the following contributions per product category:
\$1.48 for whole tom (sell price\$4.00 – (direct lab \$1.18+var OH \$0.24+var sell \$0.40+package mat \$0.70))
\$1.32 for tom juice (sell price\$4.50 – (direct lab \$1.32+var OH \$0.36+var sell \$0.85+package mat \$0.65))
\$1.85 for tom paste (sell price\$3.80 – (direct lab \$0.54+var OH \$0.26+var sell \$0.38+package mat \$0.77)) Problems with alternative 2

Just like alternative 1, tomato cost is a sunk cost at this point and not a variable cost

Another problem with Myers’ calculation is that he would need to recalculate fruit cost for juice category if he is planning to produce juice with all left over tomatoes as indicated.

The ratio of grade A to grade B tomatoes is now 3 to 2(600,000lbs A and 400,000lbs B) vs. the minimum requirement 1 to 3.
\$1.53 fruit cost per case for juice (8 lbs grade B *5.18 cent/ lb) + (12 lbs grade A*9.32 cents/lb)
This would result in (\$0.04) marginal profit per case so we can conclude that Myers’ method is not the way to go. Constraints: SOLUTION Red Brand Canners Solver: Calculate the solution. Alternative 1 Alternative 2 Without Purchased: \$213,777
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