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1. A small refinery produces only two products: Super and Diesel. These are produced by processing crude oil through three (3) processors: a cracker, a splitter and a separator. To produce one barrel of Super requires 3 hours for cracker, 2 hours for separator and splitter requires three times the hours required for cracker. To produce a barrel of Diesel requires 4 hours for splitter, half the time required for splitter is needed for cracker and five times the time required for cracker is needed for separator. The factory has allocated at most 66 hours for cracker, 180 hours for splitter and 200 labour hours for separator. In addition, it cost the producer GHC45.00 and GHC90.00 per barrel to produce Super and Diesel respectively. Selling prices per barrel of Super and Diesel are GHC135.00 and GHC165.00 respectively. a. Formulate the manufacturer's problem as LP so as to maximize profit whilst satisfying the resource limitation. b. Determine how many of each item should be produced to maximize profit; c. Determnine the scarce resources

1. A small refinery produces only two products: Super and Diesel. These are produced by processing crude oil through three (3) processors: a cracker, a splitter and a separator. To produce one barrel of Super requires 3 hours for cracker, 2 hours for separator and splitter requires three times the hours required for cracker. To produce a barrel of Diesel requires 4 hours for splitter, half the time required for splitter is needed for cracker and five times the time required for cracker is needed for separator. The factory has allocated at most 66 hours for cracker, 180 hours for splitter and 200 labour hours for separator. In addition, it cost the producer GHC45.00 and GHC90.00 per barrel to produce Super and Diesel respectively. Selling prices per barrel of Super and Diesel are GHC135.00 and GHC165.00 respectively. a. Formulate the manufacturer's problem as LP so as to maximize profit whilst satisfying the resource limitation. b. Determine how many of each item should be produced to maximize profit; c. Determnine the scarce resources

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 27EQ
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1. A small refinery produces only two products: Super and Diesel. These are produced by processing crude oil through three (3) processors: a cracker, a splitter and a separator. To produce one barrel of Super requires 3 hours for cracker, 2 hours for separator and splitter requires three times the hours required for cracker. To produce a barrel of Diesel requires 4 hours for splitter, half the time required for splitter is needed for cracker and five times the time required for cracker is needed for separator. The factory has allocated at most 66 hours for cracker, 180 hours for splitter and 200 labour hours for separator. In addition, it cost the producer GHC45.00 and GHC90.00 per barrel to produce Super and Dicsel respectively. Selling prices per barrel of Super and Diesel are GHC135.00 and GHC165.00 respectively. Formulate the manufacturer's problem as LP so as to maximize profit whilst satisfying the resource limitation. b. Determine how many of each item should be produced to maximize profit: c. Determine the scarce resources d. Find the shadow prices of the resources available to the firm. e. If there is an hour increase each in the scarce resources what will be the effect on profit? f. What output should be produced if profit on diesel increase by GHC20 per barrel. answer all
Transcribed Image Text:1. A small refinery produces only two products: Super and Diesel. These are produced by processing crude oil through three (3) processors: a cracker, a splitter and a separator. To produce one barrel of Super requires 3 hours for cracker, 2 hours for separator and splitter requires three times the hours required for cracker. To produce a barrel of Diesel requires 4 hours for splitter, half the time required for splitter is needed for cracker and five times the time required for cracker is needed for separator. The factory has allocated at most 66 hours for cracker, 180 hours for splitter and 200 labour hours for separator. In addition, it cost the producer GHC45.00 and GHC90.00 per barrel to produce Super and Dicsel respectively. Selling prices per barrel of Super and Diesel are GHC135.00 and GHC165.00 respectively. Formulate the manufacturer's problem as LP so as to maximize profit whilst satisfying the resource limitation. b. Determine how many of each item should be produced to maximize profit: c. Determine the scarce resources d. Find the shadow prices of the resources available to the firm. e. If there is an hour increase each in the scarce resources what will be the effect on profit? f. What output should be produced if profit on diesel increase by GHC20 per barrel. answer all
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