Each week Chemco can purchase unlimited quantitiesof raw material at $6/lb. Each pound of purchased rawmaterial can be used to produce either input 1 or input 2.Each pound of raw material can yield 2 oz of input 1,requiring 2 hours of processing time and incurring $2 inprocessing costs. Each pound of raw material can yield 3 ozof input 2, requiring 2 hours of processing time and incurring$4 in processing costs.Two production processes are available. It takes 2 hoursto run process 1, requiring 2 oz of input 1 and 1 oz of input 2. It costs $1 to run process 1. Each time process 1 isrun 1 oz of product A and 1 oz of liquid waste are produced.Each time process 2 is run requires 3 hours of processingtime, 2 oz of input 2 and 1 oz of input 1. Process 2 yields1 oz of product B and .8 oz of liquid waste. Process 2 incurs $8 in costs.Chemco can dispose of liquid waste in the Port CharlesRiver or use the waste to produce product C or product D.Government regulations limit the amount of waste Chemcois allowed to dump into the river to 1,000 oz/week. Oneounce of product C costs $4 to produce and sells for $11.One hour of processing time, 2 oz of input 1, and .8 oz ofliquid waste are needed to produce an ounce of product C.One unit of product D costs $5 to produce and sells for $7.One hour of processing time, 2 oz of input 2, and 1.2 oz ofliquid waste are needed to produce an ounce of product D.At most 5,000 oz of product A and 5,000 oz of productB can be sold each week, but weekly demand for productsC and D is unlimited. Product A sells for $18/oz and product B sells for $24/oz. Each week 6,000 hours of processing time is available. Formulate an LP whose solution willtell Chemco how to maximize weekly profit.
Each week Chemco can purchase unlimited quantities
of raw material at $6/lb. Each pound of purchased raw
material can be used to produce either input 1 or input 2.
Each pound of raw material can yield 2 oz of input 1,
requiring 2 hours of processing time and incurring $2 in
processing costs. Each pound of raw material can yield 3 oz
of input 2, requiring 2 hours of processing time and incurring
$4 in processing costs.
Two production processes are available. It takes 2 hours
to run process 1, requiring 2 oz of input 1 and 1 oz of input 2. It costs $1 to run process 1. Each time process 1 is
run 1 oz of product A and 1 oz of liquid waste are produced.
Each time process 2 is run requires 3 hours of processing
time, 2 oz of input 2 and 1 oz of input 1. Process 2 yields
1 oz of product B and .8 oz of liquid waste. Process 2 incurs $8 in costs.
Chemco can dispose of liquid waste in the Port Charles
River or use the waste to produce product C or product D.
Government regulations limit the amount of waste Chemco
is allowed to dump into the river to 1,000 oz/week. One
ounce of product C costs $4 to produce and sells for $11.
One hour of processing time, 2 oz of input 1, and .8 oz of
liquid waste are needed to produce an ounce of product C.
One unit of product D costs $5 to produce and sells for $7.
One hour of processing time, 2 oz of input 2, and 1.2 oz of
liquid waste are needed to produce an ounce of product D.
At most 5,000 oz of product A and 5,000 oz of product
B can be sold each week, but weekly demand for products
C and D is unlimited. Product A sells for $18/oz and product B sells for $24/oz. Each week 6,000 hours of processing time is available. Formulate an LP whose solution will
tell Chemco how to maximize weekly profit.
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