Formulate an LP model to determine the production plan that maximizes profit.
Formulate an LP model to determine the production plan that maximizes profit.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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![Blending Problems: This is another large class of problems in which linear prograrnming is applied heavily. Blending is concerned with mixing different
materials called the constituents of the mixture (these may be chemicals, gasoline, fuels, solids, colors, foods, etc.) so that the mixture conforms to
specifications on several properties or charactenistics, To model a blending problem as an LP, the linearity assumptions must hold This implies that the
value for a characteristic for the constituents in the mixtures are the weighted average of the values of that characteristic for the constituents in the mixture:
the weights being the proportions of the constituents. As an example, consider a mixture consisting of 4 barrels of fuel 1 and 6 barrels of fuel 2 and suppose
the characteristic of interest is the octane rating (Qc.R). Flinearity assumptions hold, the Oc.R of the mixture must be equal to (4 fimes the QcR of fuel 1
+6 times the OcR of fuel 2)/(4 +6). These linearity assumptions hold to a reasonable degree of precision for many important characteristics of blends of
gasolines, of crude oils, of paints, of foods, etc. That's why linear programming is used extensively in optimizing gasoline blending, in the manufacture of
paints, cattle feeds, beverages, etc. The decision variables ina blending problem are usually either the quantifies or the proportions of the constituents.
Problem,
Three liquid mixtures are to be designed as provided in the table below to contain a special chernical called "Optim
Optum [7]
45
Availability [gallons]
Cost (5/gallon]
20
Material
008
1000
15
65
30
700
1500
30
25
Minimum
Optim 7] Optim (%]
25
30
40
Maximum
Required Amount
(gallons]
600
1200
900
Selling Price ($/gallon)
70
105
140
Mixture
45
50
65
Formulate an LP model to determine the production plan that maximizes profit.
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Transcribed Image Text:Blending Problems: This is another large class of problems in which linear prograrnming is applied heavily. Blending is concerned with mixing different
materials called the constituents of the mixture (these may be chemicals, gasoline, fuels, solids, colors, foods, etc.) so that the mixture conforms to
specifications on several properties or charactenistics, To model a blending problem as an LP, the linearity assumptions must hold This implies that the
value for a characteristic for the constituents in the mixtures are the weighted average of the values of that characteristic for the constituents in the mixture:
the weights being the proportions of the constituents. As an example, consider a mixture consisting of 4 barrels of fuel 1 and 6 barrels of fuel 2 and suppose
the characteristic of interest is the octane rating (Qc.R). Flinearity assumptions hold, the Oc.R of the mixture must be equal to (4 fimes the QcR of fuel 1
+6 times the OcR of fuel 2)/(4 +6). These linearity assumptions hold to a reasonable degree of precision for many important characteristics of blends of
gasolines, of crude oils, of paints, of foods, etc. That's why linear programming is used extensively in optimizing gasoline blending, in the manufacture of
paints, cattle feeds, beverages, etc. The decision variables ina blending problem are usually either the quantifies or the proportions of the constituents.
Problem,
Three liquid mixtures are to be designed as provided in the table below to contain a special chernical called "Optim
Optum [7]
45
Availability [gallons]
Cost (5/gallon]
20
Material
008
1000
15
65
30
700
1500
30
25
Minimum
Optim 7] Optim (%]
25
30
40
Maximum
Required Amount
(gallons]
600
1200
900
Selling Price ($/gallon)
70
105
140
Mixture
45
50
65
Formulate an LP model to determine the production plan that maximizes profit.
888
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