Alberton Fisheries Limited (AFL) is an integrated fish

Alberton Fisheries Limited (AFL) is an integrated fish products company. AFL operates a small fleet of trawlers. When the trawlers land their catch, AFL has the choice of selling the whole (round) fish or processing the fish itself. The processing operation-begins by removing the head, tail, skin, bones, and insides of the fish (these byproducts are called offal), leaving two fillets. The fillets represent about 70% of the weight of the whole fish. All of the offal is processed into a fertilizer whose net realizable value is zero. In fact, AFL began the fertilizer manufacturing operation only to provide a means of disposing of the offal. The disposition of the fillets depends on the quality. There are three quality grades used. On average, 50% of the fillets are grade 1, 30% are grade 2, and 20% are grade 3. The grade 1 fillets are sold as fresh fish if there is a market available; otherwise they are downgraded to grade 2. The grade 2 fillets are used in the preparation of gourmet entrees that are sold directly by AFL or, under other names, by other distributors. The process involves cooking the fish and then packing the fillet with other products into a container, which is then frozen. If there is an excess supply of grade 2 fillets, the grade 2 fillets are downgraded to grade 3. The grade 3 fillets are used either to produce the processed, or so-called ketchup-carrier, line of products such as breaded fish sticks, or they are frozen into blocks to be stored for future use or sold. The processing facility can handle a maximum batch of 100,000 pounds of fish. Any trawler load in excess of this amount has to be sold at whatever price it will fetch, since, given current capacity, the excess fish would spoil before they could be processed. The cost of processing a batch of fish consists of two components. There is a variable cost of $0.30 per pound of whole fish processed. This cost relates entirely to the unloading and filleting operations and is comprised of wages paid to the factory workers, as well as variable overhead. In addition, there is a fixed cost of $15,000 per batch processed relating to factory depreciation, administrative charges, and salaries. For fish sold fresh, the only additional costs beyond filleting are the packaging costs, which average $0.10 per pound, and the shipping and handling costs, which average $1.00 per pound. AFL is currently receiving $2.50 per pound of fresh fish. The maximum amount of fish that can be cooked and frozen per batch is 40,000 pounds. The cost of cooking and freezing is about $0.20 per pound of fish irrespective of whether the fish will be sold as an entree or as a processed product. For the entree products, the average cost of additional items included with the fish is $1.00 per pound of fish packaged, and the packaging cost is $0.20 per pound of fish. Since the entrees, the processed fish products, and the frozen blocks are sold F.O.B. AFL's factory, there are no shipping costs associated with any of these products. AFL is currently receiving $2.40 per pound of fish sold as an entree. For the processed products, the average cost of additional material included with the fish is $0.10 per pound of fish packaged, and the packaging cost is about $0.10 per pound of fish. AFL is currently receiving $1.30per pound of fish sold as a processed food product. The cost of freezing the fillets into blocks is about $0.10 per pound. The current market price for frozen blocks is about $0.70. The production manager has advised the marketing manager that she can use about 10,000 pounds of frozen blocks next week and will be willing to pay up to $0.80 per pound for the blocks.

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The captain of one of the trawlers has just radioed in that he will land in two hours with about 110,000 pounds of fish. The marketing manager, has advised you that he can sell a maximum of 40,000 pounds of whole fish, 20,000 pounds of fresh fish, 28,000 pounds of fish as entrees, 30,000 pounds of fish as processed, and 20,000 pounds of fish sold in frozen blocks. (The last amount excludes the 10,000 that the production manager said she would take.) The marketing manager has also advised you that whole fish can be sold at a price of $0.50 per pound.

What is the optimal disposition of this catch? 

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