Red Brand Canners
And Monday, September 13, 1965, Mr. Michael Gordon, Vice President of operations, asked the Controller William Cooper, the Sales Manager Charles Myers, and Dan Tucker the Production Manager to meet with him to discuss the amount of tomato products to pack that season. The tomato crop, which had been purchased at planting, was beginning to arrive at the cannery, and packing operations would have to be started by the following Monday. Red Brand Canners (RBC) was a medium-size company that canned and distributed a variety of fruit and vegetable products under private brands in the western states.
Cooper and Myers were the first to arrive in Mr. Gordon‟s office. The production
manager came in a few minutes later and said that he had picked up produce inspection‟s
latest estimate of the quality of the incoming tomatoes. According to their report, about 20% of the crop was grade „A‟ quality and the remaining portion of the 3 million pound
crop was grade „B‟.
Gordon asked Myers about the demand for tomato products for the coming year. Myers replied that they could sell all of the whole canned tomatoes they could produce. The expected demand for tomato juice and tomato paste, on the other hand, was limited. The sales manager then passed around the latest demand forecasts, which is shown in Exhibit 1. He reminded the group that the selling price has been set in light of the long-term marketing strategy of the company, and potential sales have been forecasted at these prices.
Bill Cooper, after looking at Myers‟ estimates of demand said that it looked like the company “should do quite well on the tomato crop this year.” With the new accounting system that had been set up, he has been able to compute the contribution for each products, and according to his analysis the incremental profit on the whole tomatoes was greater than for any other tomato products. In May, after RBC had signed contracts agreeing to purchase the grower‟s production at an average delivered price of $0.18 per
pound, Cooper had computed the tomato products‟ contributions (see Exhibit 2).
Dan Tucker brought to Cooper‟s attention that although there was ample production capacity, it was impossible to produce all whole tomatoes because too small portion of the tomato crop was „A‟ quality. RBC used a numerical scaling to record the quality of both raw produce and prepared products. This scale ran from 0 to 10, with the higher number representing better quality. Rating tomatoes according to this scale, grade „A‟
tomatoes averaged 9 points per pound and grade B tomatoes averaged 5 points per pound. Tucker noted that the minimum average input quality for canned whole tomatoes was 8 and for juice it was 6 points per pound. Paste could be made entirely from grade „B‟ tomatoes. This meant that whole tomato production was limited to 800,000 pounds.
Gordon stated that this was not a real limitation. He had been recently solicited to purchase 80,000 pounds of grade „A‟ tomatoes at $0.085 per pound and at that time he
turned down the offer. He felt, however, that the tomatoes were still available.
Myers, who had been doing some calculations, said that although he agreed that the company “should do quite well this year” it would not be by canning whole tomatoes. It seemed to him that the tomato cost should be allocated based on quantity and quality, rather than by quantity only as Cooper had done. Therefore, he re-computed the marginal profit on this basis (Exhibit 3). From his result, RBC should use 2,000,000 pounds of the grade „B‟ tomatoes for paste, and the remaining 400,000 pounds of grade „B‟ along with all of the 600,000 pounds of grade „A‟ tomatoes for juice.
Answer the following questions:
1. Why does Tucker state that the whole tomato production is limited to 800,000 pounds?
(i.e. where does the number 800,000 come from?)
2. What is wrong with Cooper‟s suggestion to use the entire crop for whole tomatoes?
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?
Set up a linear programming model and solve it with Solver. Answer sensitivity analysis questions:
4. Without including the possibility of the additional purchases suggested by Gordon,
formulate as an LP the problem of determining the optimal canning policy. Use the
appropriate parameters from one of the exhibits shown below.
5. Answer the following questions about the optimal solution:
a. How much of each tomato grade will be used for the production of each
b. How much of each product is produced?
c. What is the actual average quality per pound of the whole tomato and the
d. What is the net profit obtained after netting out the cost of the crop? 6. Answer the following sensitivity analysis questions:
a. Is additional purchase of up to 80,000 pounds of grade „A‟ should be
undertaken at a price of $0.085? Can you tell exactly how much should be
b. Suppose the Market Research Department feels that it can increase
demand for the juice product by 25,000 cases by starting an advertising
campaign. How much should RBC be willing to pay for such a campaign?
c. Suppose the price of juice increased 30 cents per case. What will happen
to the optimal solution?
d. Suppose an additional lot of 50,000 pounds of grade „B‟ tomatoes
becomes available. How much should RBC be willing to pay for this lot?
It was just one day before your report was ready when VP Gordon called you and raised a concern he had for quite sometime in regard to the forecast of demand for tomato paste. He reminded you that the forecasts for the tomato paste demand in the last few years caused problems of either too much production or too little, in a way that costs the company either extensive holding costs or reduced sales. He asked you to be conservative in your suggested production plan for the coming year, and added he was particularly interested in three demand profiles for the tomato paste: 70,000, 80,000, and 90,000 cases. This was of course a bump in the road. Myers and Tucker had no clue how to even start, while Cooper suggested you use the holding cost of $1.8 per case of tomato paste calculated last year, applied to each unsold unit. He also offered a penalty of $25 per case for each case out of stock. “Mr. Myers”, you almost yelled, “then we need to include
penalties on both whole tomato and tomato juice, because we don‟t know whether all the
demand for these items is going to be satisfied.” “I am not Myers; this is Cooper. And yes,
young man, the penalty on a case of whole tomato should be $1.5 and this of tomato juice $2.00”.
Now it remained your job to re-formulate the linear programming model, that will provide an optimal production plan as before, while incorporating all the possible scenarios of the tomato paste demand and conservatively deal with this kind of uncertainty.
Exhibit 1: Demand forecasts and usage Demand Pound Product Forecast (cases) per case Whole Tomato 800,000 18 Tomato Juice 50,000 20 Tomato Paste 80,000 25
Exhibit 2: Cooper's product item profitability Whole Tomato Tomato Product Tomatoes Juice Paste Selling price $12 $13.50 $11.40 Variable costs: Direct labor 3.54 3.96 1.62 Variable OHD 0.72 1.08 0.78
Variable Selling 1.2 2.55 1.14
Packaging 2.1 1.95 2.31
Tomato 3.24 3.6 4.5 Total Variable costs 10.8 13.14 10.35
Contribution 1.2 0.36 1.05
Less Allocated OHD 0.84 0.63 0.69 Net Profit 0.36 -0.27 0.36
Exhibit 3: Myers' Marginal Analysis Calculating the actual cost of grade 'A' and grade 'B' tomatoes:
Z = Cost per pound of 'A' tomato in cents
Y = Cost per pound of 'B' tomato in cents (1) 600,000Z+2,400,000Y = (3,000,000)(18cent) (2) ZY ; 95 Z = 27.96 cents Y = 15.54 cents
Whole Tomato Tomato Product Tomatoes Juice Paste Selling Price $12.00 $13.50 $11.40 Variable cost $7.56 $9.54 $5.85 (excluding Tomato
4.44 3.96 5.53 Tomato cost $4.47 $3.72 $3.90 Marginal Profit ($0.03) $0.24 $1.65