1.Based on the availability of 600,000 pounds of grade “A” tomatoes (grade 9), one can mix in some grade “B” tomatoes (grade 5) to generate a mix of grade 8. Let X denote the pounds of grade “B” tomatoes that can be mixed in. Then: (600,000*9+X*5)/(600,000+X)=8.
Solving this, yields X=200,000 lbs for a total weight of 800,000 lbs.
2.Cooper’s suggestion restricts the usage of tomatoes to merely 800,000 lbs (as shown in 1). The leftover tomatoes could be used profitably to at least make tomato paste. It might also be more profitable to make use of the A tomatoes to produce some tomato juice as well, and end up with a mix products that together produce the most profit.
3.In Exhibit 3, Myers attempt to prorate the unit cost per tomato (18 cents) based on the quality of tomato (grade A or B). The first equation (1) indicates that the sum of 600,000 lb multiplied by the unit cost per lb for grade A tomatoes (Z) and 2,400,000 lb multiplied by the unit cost per lb for grade B tomatoes (Y) equals the total cost paid (3,000,000 lbs multiplied by 18 cents per lb). The second equation (2) defines the relative relationship between the unit prices for grade A and B tomatoes based on the relative “quality” points for the two grades. Solving the two equations yields the values for the unit prices for the two grades.
Based on this one can state that the unit cost per lb for tomatoes of “quality of 1” is equal to the value of Z/9 or Y/5. This is then used to find the adjusted fruit cost. For example, the cost per case of whole tomatoes would be: (Z/9) $/lb *8*18 lb/case or $4.47 per case. Similarly, for tomato juice the cost per case would be: (Z/9) $/lb * 6 * 20 lb/ case = $3.72 per case. Since Myers believes that tomato paste is the most profitable option, he would like to sell as much tomato paste that demand allows, which is 80,000 cases or 2,000,000 lbs (80,000 cases*25lb per case). Beyond that Myers ranks...