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RED BRAND CANNERS Case Analysis by Group 10, Section E Case Summary:
Red Brand Canners was a medium-size company which canned and distributed a variety of fruit and vegetable products under private brands in the western states. Mr. Gordon was the VP, Operations who wanted to formulate the future strategy of packing tomato products with Mr. William Cooper, Controller, Mr. Myers, Sales Manager and Mr. Dan Tucker, Production Manager. There were two grades of tomatoes according to the inspection done by Mr. Cooper: 1.
Grade A : 20% of 3,000,000 = 6,00,000 pounds
Grade B : 80% of 3,000,000 = 24,00,000 24,00,000 pounds
Mr. Myers provided demand forecast and pre-set selling prices as per the long term marketing strategy of the company. Three types of Tomato products were produced by the company – Whole tomatoes, Tomato Juice, Tomato paste. Mr. Cooper produced the computed tomato products’ contributions based on the purchase of tomatoes at an average delivery price of 6 cents per pound. Mr. Dan Tucker brought the various constraints with respect to ratings on the quality of tomatoes and their eff ect ect on production. According to the company’s scale, ‘A’ tomatoes averaged 9 points per pound and ‘B’ tomatoes averaged 5 points per pound. Minimum average input quality for canned whole
tomatoes and juice was 8 and 6 points per pound respectively. According to Mr. Gordon, this wasn’t a real limitation as an additional 80,000 pounds of Grade ‘A’ tomatoes could be bought at 8.5 cents per pound. Mr. Myers formulated the relevant numbers again on the basis of quality and quantity unlike Mr. Cooper’s work and proposed that Red Brand should use 2,000,000 pounds of ‘B’ tomatoes for paste and remaining 400,000 pounds of ‘B’ tomatoes and all of the ‘A’ tomatoes for juice. According to him, this
proposal if implemented would lead to a contribution of $48,000 from this year’s tomato crop. Problem Statements:
To find the objective function maximising the profit garnered through production of various type of tomato based products. To decide on the purchase of additional 80,000 pounds of Grade A tomatoes at 8.5 cents as proposed by Gordon. To check whether the solution proposed by Myers is the optimal solution considering all the given constraints. 1
Our take on the problem: Case 1: Maximization of profit taking optimum mix of tomato products Decision Variables:
Tomato products coming from both the available grades of tomato crops i.e. Grade A and Grade B. As there are 3 different types of Tomato products available in the f orm of Canned Whole Tomatoes, Tomato Juice and Tomato Paste. Hence in all 6 decision variables are taken. They are: Xa: Weight of “Canned Whole Tomatoes” produced from Grade A tomato crops. Xb: Weight of “Canned Whole Tomatoes” produced from Grade B tomato crops. Ya: Weight of “Tomato Juice” produced from Grade A tomato crops.
Yb: Weight of “Tomato Juice” produced from Grade B tomato crops. Za: Weight of “Tomato Paste” produced from Grade A tomato crops. Zb: Weight of “Tomato Paste” produced from Grade B tomato crops.
From Exhibit 2: Contribution coming from each tomato product per case: Contribution from Whole Tomatoes: $ 1.48 / 18 = $ 0.082 Contribution from Tomato Juices: $ 1.32 / 20 = $ 0.066 Contribution from Tomato Paste: $ 1.85 / 25 = $ 0.074 Objective Function:
F = 0.082*( Xa + Xb ) + 0.066*( Ya + Yb ) + 0.074*( Za + Zb ) – FC
(In this case FC is: 3000000*6 cents)
Quantity of Incoming Tomato Crop: Grade A = 20% of 3000000= 600000 Grade B = 80% of 3000000=2400000 Hence, Xa+ Ya +Za <= 600000 & Xb +Yb +Zb <= 2400000 Total Weight: Whole Tomatoes: Xa + Xb <= 14400000
(800000*18 from exhibit 1 and 2)
: Ya + Yb <= 1000000
(50000*20 from exhibit 1 and 2)
Tomato Pastes : Za + Zb <= 2000000
(80000*25 from exhibit 1 and 2)
By Mr. Tuckers Remarks: Xa- 3*Xb >= 0 2
3*Ya –Yb >= 0 Zb >= 0 Putting the objective function with decision variables along with Constraints in Excel we will be able to get the optimize solution in terms of maximum profit. Case 2: Whether Extra 80000 tomato crops of Grade A has to be bought or not.
With the meaning of variables remaining same as in Case 1: New Objective Function:
F = 0.082*( Xa + Xb ) + 0.066*( Ya + Yb ) + 0.074*( Za + Zb ) – FC (In this case FC is: 3000000*6 cents +80000*8.5 cents) Constraints:
Quantity of Incoming Tomato Crop: Grade A = 20% of 3000000= 600000 + 80000 (to be bought from another source ) Grade B = 80% of 3000000=2400000 Hence, Xa+ Ya +Za <= 680000 & Xb +Yb +Zb <= 2400000 Total Weight: Whole Tomatoes: Xa + Xb <= 14480000 Tomato Juices
: Ya + Yb <= 1000000
Tomato Pastes : Za + Zb <= 2000000 We can solve this LPP (Linear Programming Problem) with solver and then verify that whether the decision to purchase additional 80000 Grade A crops should be taken or not. Case 3: Myers Solution: Whether Optimal or not His idea: 2 million Grade B tomatoes for paste, and remaining grade A and B for juice.
Contribution: 2000000*0.074 + (40000 + 60000)*0.066 =$ 214000 Cost: 3000000* 6 cents= $ 180000 Profit: $ 214000 – 180000 = $ 34000 This profit needs to be compared with Optimal Profit obtained above using Solver. I f the optimal profit obtained is more than $ 34000 then his suggestion should not be incorporated.