the two products that case chemical makes- cs01 and cs02 yield excessive
amounts of three different pollutants: a,b,and c. the state government
has ordered the company to install and to employ antipollution devices.
the following table provides the current daily emissions in
kg/1000liters and the maximum of each pollutant allowed in kg.
pollutant======cs01========cs02=====max allowed
A ============ 25 ========40 ====== 43
B ============ 10 ======== 15 ======20
C ============ 80 ======== 60 ======50
the manager of the production department has approved the installation
of two antipollution devices. the emissions from each product can be
handled by either device in any proportion. ( the emissions are sent
through a device only once, that is, the output of one device cannot be
the input to the other or back to itself). The following table shows the
percentage of each pollutant from each product that is removed by each
device.
============device 1============device2
pollutant === cs01 cs02 ========== cs01 cs02
A ===========40 === 40 =========== 30==== 20
B ===========60==== 60 =========== 0 ==== 0
C ===========55==== 55 =========== 65==== 80
For example, if the emission from cs01 is sent through device 1, 40% of
pollutant A, 60% of pollutant B, and 55 % of pollutant C are removed.
Manufacturing considerations dictate that cs01 and cs02 be produced in
the ratio of 2 to 1.
Formulate a LP model to determine a plan that maximizes the total daily
production ( amount of cs01 plus amount of CS02) while meeting gov
require
Mathematics Homework Solutions
#7944
Linear Programming Problem: Maximizing Productivity
The two products that case chemical makes- cs01 and cs02 yield excessive amounts of three different pollutants: a,b,and c. the state government has ordered the company to install and to employ antipollution devices. the following table provides the current daily emissions in kg/1000liters and the maximum of each pollutant allowed in kg.
pollutant======cs01========cs02=====max allowed
A ============ 25 ========40 ====== 43
B ============ 10 ======== 15 ======20
C ============ 80 ======== 60 ======50
the manager of the production department has approved the installation of two antipollution devices. the emissions from each product can be handled by either device in any proportion. ( the emissions are sent through a device only once, that is, the output of one device cannot be the input to the other or back to itself). The following table shows the percentage of each pollutant from each product that is removed by each device.
============device 1============device2
pollutant cs01 cs02 cs01 cs02
A ===========40 === 40 =========== 30==== 20
B ===========60==== 60 =========== 0 ==== 0
C ===========55==== 55 =========== 65==== 80
For example, if the emission from cs01 is sent through device 1, 40% of pollutant A, 60% of pollutant B, and 55 % of pollutant C are removed. Manufacturing considerations dictate that cs01 and cs02 be produced in the ratio of 2 to 1.
Formulate a LP model to determine a plan that maximizes the total daily production ( amount of cs01 plus amount of CS02) while meeting gov requirements.
Linear programming is used tosolve a pollution related problem. The solution is detailed and well presented.
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