(This problem comes from Winston and Venkataramanan, originally from Sulli-van a
ID: 2956381 • Letter: #
Question
(This problem comes from Winston and Venkataramanan, originally from Sulli-van and Secrest.) Lizzie's Dairy produces cream cheese and cottage cheese. Milk and cream are blended to produce these two products. Both high-fat and low-fat milk can be used to produce cream cheese and cottage cheese. High-fat milk is 60% fat; low-fat milk is 30% fat. The milk used to produce cream cheese must average at least 50% fat, and that for cottage cheese at least 35% fat. At least 40% (by weight) of the inputs to cream cheese and at least 20% (by weight) of the inputs to cottage cheese must be cream. Both cream cheese and cottage cheese are produced by putting milk and cream through the cheese machine. It costs $0:40 to process 1 lb of inputs into into a pound of cream cheese. It costs $0:40 to produce 1 lb of cottage cheese, but every pound of input for cottage cheese yields 0:9 lb of cottage cheese and 0:1 lb of waste. Cream is produced by evaporating high-fat and low-fat milk. It costs $0:40 to evaporate 1 lb of high-fat milk, and each pound of high-fat milk that is evaporated yields 0:6 lb of cream. It costs $0:40 to evaporate 1 lb of low-fat milk, and each pound of low-fat milk that is evaporated yields 0:3 lb of cream. Each day, up to 3000 lb of input may be sent through the cheese machine. Each day, at least 1000 lb of cream cheese and 1000 lb of cottage cheese must be produced. Up to 1500 lb of cream cheese and 2000 lb of cottage cheese can be sold each day. Cream cheese is sold for $1:50 per lb and cottage cheese for $1:20 per lb. High-fat milk is purchased for $0:80 per lb, and low-fat milk for $0:40 per lb. The evaporator can process at most 2000 lb of milk daily. Formulate a linear program in canonical form that can be used to maximize Lizzie's daily profit. In particular, provide the matrix A and vectors b and c for the LP. It will be helpful to declarex1 = lb of high-fat milk that will go to cream cheese in cheese machine
x2 = lb of low-fat milk that will go to cream cheese in cheese machine
x3 = lb of cream that will go to cream cheese in cheese machine
x4 = lb of high-fat milk that will go to cottage cheese in cheese machine
x5 = lb of low-fat milk that will go to cottage cheese in cheese machine
x6 = lb of cream that will go to cottage cheese in cheese machine
x7 = lb of high-fat milk that will go to cream
x8 = lb of low-fat milk that will go to cream.
Explanation / Answer
http://www.engineering.uiowa.edu/~dbricker/OR_Sample_Quizzes/Quizzes_F97.pdf
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