How large would x have to be in order to make it profitable for the plant to sell fresh bellies? How about for picnics?
How would the sales of small amounts of fresh bellies and picnics affect the rest of the operation?
What precisely do "small amounts" mean in this context?
(Chvatal 1.6, adapted from Greene et al. (1957)) A meat packing plant produces 480 hams, 400 pork bellies, and 230 picnic hams every day, each of these products can be sold either fresh or smoked. The total number of hams, bellies, and picnics that can be smoked during a normal working day is 420; in addition up to 250 products can be smoked on overtime at a higher cost. The net profits are as follows: Smoked on Smoked on Fresh regular time overtime Hams $8 $14 $11 Bellies $4 $12 $7 Picnics $4 $13 For example, the following schedule yields a total net profit of $9.965: Smoked on Smoked on Fresh regular time overtime Hams 165 280 35 Bellies 295 Picnics 105 $9 35 70 70 55 (Chvatal 5.6) In the optimal solution to problem 1, all the bellies and picnics are smoked. However, sufficiently drastic changes in the market prices might provide an incentive to change this policy. Assume that the market price of fresh bellies increases by x dollars, while all the other prices remain fixed at their original levels. a) How large would x have to be in order to make it profitable for the plant to sell fresh bellies? b) Ask and answer a similar question for picnics. c) How would the sales of small amounts of fresh bellies and picnics affect the rest of the operation? d) What precisely do "small amounts" mean in this context? (Chvatal 1.6, adapted from Greene et al. (1957)) A meat packing plant produces 480 hams, 400 pork bellies, and 230 picnic hams every day, each of these products can be sold either fresh or smoked. The total number of hams, bellies, and picnics that can be smoked during a normal working day is 420; in addition up to 250 products can be smoked on overtime at a higher cost. The net profits are as follows: Smoked on Smoked on Fresh regular time overtime Hams $8 $14 $11 Bellies $4 $12 $7 Picnics $4 $13 For example, the following schedule yields a total net profit of $9.965: Smoked on Smoked on Fresh regular time overtime Hams 165 280 35 Bellies 295 Picnics 105 $9 35 70 70 55 (Chvatal 5.6) In the optimal solution to problem 1, all the bellies and picnics are smoked. However, sufficiently drastic changes in the market prices might provide an incentive to change this policy. Assume that the market price of fresh bellies increases by x dollars, while all the other prices remain fixed at their original levels. a) How large would x have to be in order to make it profitable for the plant to sell fresh bellies? b) Ask and answer a similar question for picnics. c) How would the sales of small amounts of fresh bellies and picnics affect the rest of the operation? d) What precisely do "small amounts" mean in this context
