
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
expand_more
expand_more
format_list_bulleted
Question
thumb_up100%
Constraints are in the statement and charts
![Blending Problems: This is another large class of problems in which linear programming 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 characteristics. 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 (Oc.R). If linearity assumptions hold, the Oc.R of the mixture must be equal to (4 times the Oc.R of fuel 1
+ 6 times the Oc.R 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 in a blending problem are usually either the quantities or the proportions of the constituents.
Problem:
Three liquid mixtures are to be designed as provided in the table below to contain a special chemical called "Optim"
Optim [%]
45
35
65
30
Availability [gallons]
800
1000
Cost [$/gallon]
20
15
30
25
Material
700
1500
Minimum
Optim [%] Optim [%]
25
30
40
Required Amount
Igallons]
600
1200
Maximum
Selling Price ($/gallon)
70
Mixture
45
50
65
105
140
Y
900
Formulate an LP model to determine the production plan that maximizes profit.
1234](https://content.bartleby.com/qna-images/question/388a9fab-648d-450d-a1a5-3932044f3fea/314a6a1d-6655-463b-8532-501b72fa5aaa/dvw1zo_thumbnail.jpeg)
Transcribed Image Text:Blending Problems: This is another large class of problems in which linear programming 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 characteristics. 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 (Oc.R). If linearity assumptions hold, the Oc.R of the mixture must be equal to (4 times the Oc.R of fuel 1
+ 6 times the Oc.R 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 in a blending problem are usually either the quantities or the proportions of the constituents.
Problem:
Three liquid mixtures are to be designed as provided in the table below to contain a special chemical called "Optim"
Optim [%]
45
35
65
30
Availability [gallons]
800
1000
Cost [$/gallon]
20
15
30
25
Material
700
1500
Minimum
Optim [%] Optim [%]
25
30
40
Required Amount
Igallons]
600
1200
Maximum
Selling Price ($/gallon)
70
Mixture
45
50
65
105
140
Y
900
Formulate an LP model to determine the production plan that maximizes profit.
1234
Expert Solution

arrow_forward
Step 1
Step by stepSolved in 7 steps with 6 images

Knowledge Booster
Similar questions
- 1. Graph the system of inequalities representing the constraints.arrow_forwardDetermine graphically the solution set for the system of inequalities. x + y ≤ 5 0 ≤ x ≤ 2 y ≥ 0arrow_forwardWrite the constraint below as a linear inequality. A canoe requires 3 hours of fabrication and a rowboat 5 hours. The fabrication department has at most 112 hours of labor available each week. Let x be the number of canoes and let y be the number of rowboats. Choose the inequality that represents the given constraint. A. 3x+5y2112 B. 5x + 3y ≤ 112 C. 5x+3y2112 D. 3x+ 5y ≤ 112arrow_forward
- please help me outarrow_forwardI need explaination and spreadsheet with formulas and step to step interpretation please.....The attached are first two pages of required assisance and below is the rest of instructions please consider all of them:c. Suppose the CEO says, “Projects 3 and 4 must be undertaken but not both.”Describe the constraint.d. Suppose the CEO says, “Projects 4 cannot be undertaken unless projects 1 and 3also are both undertaken.” Describe the constraints. Hint: You may need to add more than one constraint for this part.3. [45pts] Multi-product Production Planning. Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows:Department Product 1 Product 2 Product 3A 1.50 3.00 2.00B 2.00 1.00 2.50C 0.25 0.25 0.25During the next production period, the labor-hours…arrow_forwardDefine the variables, determine the constraints and the objective function.arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat...Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEY
- Mathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,

Advanced Engineering Mathematics
Advanced Math
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Wiley, John & Sons, Incorporated

Numerical Methods for Engineers
Advanced Math
ISBN:9780073397924
Author:Steven C. Chapra Dr., Raymond P. Canale
Publisher:McGraw-Hill Education

Introductory Mathematics for Engineering Applicat...
Advanced Math
ISBN:9781118141809
Author:Nathan Klingbeil
Publisher:WILEY

Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,

