Formulate but do not solve the following exercise as a linear programming problem.Kane Manufacturing has a division that produces two models of fireplace grates, model A and model B. To produceeach model A grate requires 4 lb of cast iron and 6 min of labor. To produce each model B grate requires 5 lb of castiron and 3 min of labor. The profit for each model A grate is $2.00, and the profit for each model B grate is $1.50. If1,100 tb of cast iron and 20 hr of labor are available for the production of grates per day, how many grates of eachmodel should the division produce per day in order to maximize Kane's profits?Minimize 2x3 subject to 4x+ 5y<1,100, 6x-3y 5 1,200, x>0, y>0Maximize 2x3 subject to 4x+ 5y<1,100, 6x+³y ≤ 1,200, x 20, y 20Maximize P2x+y subject to 4x+ 5y 5 1.100, dx-3y <1,200, x20, y20Maximize P2x+3y subject to 4x5y 5 1.100, dx-3y 5 1,200, x20, y 20Minimize 2x3 subject to 4+ 5 5 1,100, 6x-3y 5 1,200, x20, y 20

Answered: Image /qna-images/answer/13075a2e-320a-48c6-af3b-08058e0e1adf.jpg

Answered: Formulate but do not solve the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

P.nil
Solve the following linear programming problem. You are taking two dietary supplements daily: Supplement A and Supplement B. An ounce of supplement A contains 9 units of calcium, 8 units of vitamin D, and 5 units of sodium. An ounce of supplement B contains 2 units of calcium, 4 units of vitamin D, and 3 units of sodium. Your goal is to get at least 90 units of calcium and at least 120 units of vitamin D from the supplements daily, while at the same time reducing the amount of sodium that you will get. How many ounces of each supplement should you take daily to reach your goals? Ounces of Supplement A = Blank 1. Fill in the blank, read surrounding text. Ounces of Supplement B = Blank 2. Fill in the blank, read surrounding text. How many units of sodium will you get daily under these circumstances? Units of Sodium = Blank 3. Fill in the blank, read surrounding text.
Formulate but do not solve the problem.The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $44 and $28 per acre, respectively. Jacob Johnson has $17,200 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? (Let x and y denote the number of acres of corn and wheat, respectively.) = 500 = 17,200
Formulate a system of equations for the situation below and solve.A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table. Sleeveless Short-Sleeve Long-Sleeve Cutting 9 12 15 Sewing 22 24 28 Packaging 6 8 8 The cutting, sewing, and packaging departments have available a maximum of 87, 176, and 52 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? sleeveless      ___ dozen short-sleeve      ___ dozen long-sleeve      ___dozen
Formulate a system of equations for the situation below and solve.A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table. Sleeveless Short-Sleeve Long-Sleeve Cutting 9 12 15 Sewing 22 24 28 Packaging 6 8 8 The cutting, sewing, and packaging departments have available a maximum of 87, 176, and 52 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? sleeveless      ___ dozen short-sleeve      ___dozen long-sleeve      ___ dozen
Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. In a certain week, the company has 2800 board feet of wood available and 560 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize      P =      subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0
Write the transportation problem as a linear programming problem in terms and solvent of x and y and solve. (Indicate the number of units that should be transported from each factory to each depot and the total transportation cost.)
Muir Manufacturing produces two popular grades of commercial carpeting among its many other products. In the coming production period, Muir needs to decide how many rolls of each grade should be produced in order to maximize profit. Each roll of Grade X carpet uses 50 units of synthetic fiber, requires 25 hours of production time, and needs 20 units of foam backing. Each roll of Grade Y carpet uses 40 units of synthetic fiber, requires 28 hours of production time, and needs 15 units of foam backing. The profit per roll of Grade X carpet is $200, and the profit per roll of Grade Y carpet is $160. In the coming production period, Muir has 3000 units of synthetic fiber available for use. Workers have been scheduled to provide at least 1800 hours of production time (overtime is a possibility). The company has 1500 units of foam backing available for use. What are the binding constraints of the feasible region of the optimal solution? Constraint 2 only Constraint 1 only…
Formulate but do not solve the following exercise as a linear programming problem.A division of the Winston Furniture Company manufactures x dining tables and y chairs. Each table requires 40 board feet of wood and 2 labor-hours. Each chair requires 16 board feet of wood and 5 labor-hours. In a certain week, the company has 2800 board feet of wood available and 500 labor-hours.If the profit for each table is $50 and the profit for each chair is $18, how many tables and chairs should Winston manufacture to maximize its profits P in dollars? Maximize P = subject to the constraints board feet labor-hours x ≥ 0 y ≥ 0
Formulate a linear programming problem that can be used to solve the following question. An individual needs a daily supplement of at least 380 units of vitamin C and 64 units of vitamin E and agrees to obtain this supplement by eating two foods, I and II. Each ounce of food I contains 34 units of vitamin C and 4 units of vitamin E, while each ounce of food II contains 20 units of vitamin C and also 12 units of vitamin E. The total supplement of these two foods must be at most 29 ounces. Unfortunately, food I contains 22 units of cholesterol per ounce and food II contains 32 units of cholesterol per ounce. Find the appropriate amounts of the two food supplements so that cholesterol is minimized. X = ---Select--- y = --Select--- ---Select--- | F = Subject to (objective function) (total ounces of food) (units of vitamin C) (units of vitamin E) x ---Select--- 0, y ---Select--- 0 (nonnegativity constraint)

Recommended textbooks for you

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

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,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS