Model the following decision-making situation as a linear program. A company makes a blend consisting of two chemicals, 1 and 2, in the ratio 5:2 by weight. These chemicals can be manufactured by three different processes using two different raw materials and a fuel. Production data are given in the table below. For how much time should each process be run in order to maximize the total amount of che blend manufactured? Requirements per unit time Output per unit time Fuel Chem 1 (units) (units) Raw 1 Raw 2 Chem 2 Process (units) (units) (units) 1 5 50 9. 2 6 8 75 7 10 3 4 11 100 10 6 Available 200 400 1850 (a) Clearly define the decision variables. (b) Write the objective function. (c) Write the constraints.
Model the following decision-making situation as a linear program. A company makes a blend consisting of two chemicals, 1 and 2, in the ratio 5:2 by weight. These chemicals can be manufactured by three different processes using two different raw materials and a fuel. Production data are given in the table below. For how much time should each process be run in order to maximize the total amount of che blend manufactured? Requirements per unit time Output per unit time Fuel Chem 1 (units) (units) Raw 1 Raw 2 Chem 2 Process (units) (units) (units) 1 5 50 9. 2 6 8 75 7 10 3 4 11 100 10 6 Available 200 400 1850 (a) Clearly define the decision variables. (b) Write the objective function. (c) Write the constraints.
Chapter6: Systems Of Equations And Inequalities
Section: Chapter Questions
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Transcribed Image Text:Model the following decision-making situation as a linear program.
A company makes a blend consisting of two chemicals, 1 and 2, in the ratio 5:2 by
weight. These chemicals can be manufactured by three different processes using two
different raw materials and a fuel. Production data are given in the table below. For
how much time should each process be run in order to maximize the total amount of
the blend manufactured?
Requirements per unit time Output per unit time
Fuel Chem 1
(units)
Raw 1
Raw 2
Chem 2
(units) (units)
(units)
(units)
6.
Process
1
9.
5
50
2
6
75
7
10
4
11
100
10
Available
200
400
1850
(a) Clearly define the decision variables.
(b) Write the objective function.
(c) Write the constraints.
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