SAMCIS Chemicals produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demands for the coming month, SAMCIS management specified that the combined production for products A and B must total to at least 350 gallons. Separately, a major customer's order of 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon and product B requires 1 hour of processing time per gallon. For the coming month, 600 hours of processing time are available. SAMCIS's objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 per gallon for product B. Generate the mathematical model for the optimal number of product A and B to be produced by SAMCIS chemicals.
SAMCIS Chemicals produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demands for the coming month, SAMCIS management specified that the combined production for products A and B must total to at least 350 gallons. Separately, a major customer's order of 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon and product B requires 1 hour of processing time per gallon. For the coming month, 600 hours of processing time are available. SAMCIS's objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 per gallon for product B. Generate the mathematical model for the optimal number of product A and B to be produced by SAMCIS chemicals.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Transcribed Image Text:SAMCIS Chemicals produces two products that are sold as raw materials to
companies manufacturing bath soaps and laundry detergents. Based on an analysis
of current inventory levels and potential demands for the coming month, SAMCIS
management specified that the combined production for products A and B must
total to at least 350 gallons. Separately, a major customer's order of 125 gallons of
product A must also be satisfied. Product A requires 2 hours of processing time per
gallon and product B requires 1 hour of processing time per gallon. For the coming
month, 600 hours of processing time are available. SAMCIS's objective is to satisfy
these requirements at a minimum total production cost. Production costs are $2 per
gallon for product A and $3 per gallon for product B. Generate the mathematical
model for the optimal number of product A and B to be produced by SAMCIS
chemicals.
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