Problem: You are in business of producing and selling 100-pound bags of health food for pet pigs. You plan to advertise that each bag will provide a pig its minimum weekly requirements of protein (200 grams), calcium (300 grams) and fiber (100 grams), and will contain no more than 500 calories. You have found supplies at a reasonable cost for three possible ingredients.
cost protein calcium fiber calories
Corn $.03/lb 100 g/lb 2 g/lb 1 g/lb 50 /lb
Fishbones $.005/lb 1 g/lb 50 /lb None 2 /lb
sawdust $.001/lb none None 200 g/lb 1 /lb
You plan to sell each bag for $1. Develop an optimization model and solve. Answer the following questions, treating each independently from the others. (You do not have to make additional solver runs; all questions may be answered from the sensitivity analysis information.)
Q1. How much would the cost of corn have to drop to make it worth adding more?
Q2. If the cost of fishbones increased to $.006 per pound, what would the impact be?
Q3. If the cost of sawdust increased to $.005 per pound, what would the impact be?
Q4. If you reduced the advertised amount of protein from 200 grams/bag to 100 grams/bag, how much would that enable you to save? Why?
Q5. If you increased the advertised proportion of fiber from 100 grams/bag to 200 grams/bag, how much would your cost increase? Why?