Red Brand Canners

1. Why does Tucker state that the whole tomato production is limited to 800,000 pounds?

The minimum average input quality for the whole canned tomato product needs to 8. Grade A tomatoes had an average quality rating of 9 whereas Grade B tomatoes had an average quality rating of 5. Available quantity of Grade A tomatoes was 600,000 lb whereas available quantity of grade B tomatoes was 2,400,000 lb. To get the average input quality of 8, the entire crop of A tomatoes had to be used and some grade B tomatoes could be mixed in the input ingredient mix.

We derived the 200,000 by working through the following equation:

X pounds of B

Total production = 600,000+X

(600,000*9)+(X*5) / (X+600,000) = 8

600,000*9 + 5X = 8X + (8*600,000)

3X=600,000

X=200,000

Thus A = 600,000 lb, B = 200,000 lb.

Total production capacity = (600,000+200,000) lb = 800,00 lb.

2. What is wrong with Cooper's suggestion to use the entire crop for the whole tomatoes?

First of all, It is impossible to produce all whole tomatoes using the entire crop of 3 million lb of different average quality ratings of tomato A and tomato B. If the entire tomato crop was to be used for whole canned tomatoes only, the average input quality would be:

{(600,000*9)+(2,400,000*5)}/(3,000,000) = 5.8

The accepted minimum average input quality of canned whole tomato had to be 8. Thus Cooper's conclusion is wrong.

Secondly, to reach his conclusion, Cooper used the contribution margin per case per product. According to his calculation:

Whole Tomatoes Tomato Juice Tomato Paste

Per case contribution $1.2 $0.36 $1.05

But Cooper used cost of tomato as a part of variable cost to calculate the contribution per case per product. As tomato cost had been incurred in the past, it is a sunk cost and cannot be a part of variable cost. Thus tomato cost should not affect contribution. Without the tomato cost the contributions per case per product are:

Whole Tomatoes Tomato Juice Tomato Paste

Per case contribution $4.44 $3.96 $5.55

Thus the contribution per case for tomato paste is the highest, not the whole tomatoes. This Copper was wrong in concluding that whole tomato had the highest contribution.

3. How does Myers reach the conclusion that the company should use 2,000,000 pounds of Grade B tomatoes for paste and the rest of the Grade B and Grade A tomatoes to produce juice? What is wrong with Myers' reasoning?

While calculating contributions per case per product, Myers reasoned that because of different quality ratings, Grade A and Grade B tomatoes should cost 27.96 cents per pound and 15.54 cents per pound respectively. In other words, cost per pound of tomato B should be 5/9th of the cost per pound of tomato A. If his new cost data is incorporated into the contribution calculation, only tomato juice and tomato paste produced positive contributions which are $0.24 and $1.65 respectively. Based on this calculation, he would only make tomato paste and tomato juice. Tomato paste generated $1.41 (1.65-0.24) more contribution per case than that of tomato juice. This is why he wanted to maximize his tomato paste production.

...