(a) For the following linear programme, sketch the feasible region and the directionof the objective function. Use you sketch to find an optimal solution to theprogram. State the optimal solution and give the objective value for thissolution.maximize +22subject to 1 + 2x2 ≤ 4,1 +3x2 ≤ 12,x1, x2 ≥0(b) For the following linear programme, sketch the feasible region and the directionof the objective function. Explain, making reference to your sketch, why thislinear programme is unbounded.maximize₁+%2subject to-2x1 + x2 ≤ 4,x1 - 2x2 ≤4,x1 + x2 ≥ 7,x1,x20Give any feasible solution to the linear programme for which the objectivevalue is 40 (you do not need to justify your answer).

Step 1: Step 2: Step 3: Step 4: Step 5: • The feasible region is unbounded because there are no…

Answered: (a) For the following linear programme,…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 37CR

See similar textbooks

Similar questions

A company manufactures two fertilizers, x and y. Each 50-pound bag of fertilizer requires three ingredients, which are available in the limited quantities shown in the table. The profit on each bag of fertilizer x is 6 and on each bag of y is 5. How many bags of each product should be produced to maximize the profit? Ingredient Number of Pounds in Fertilizer x Number of Pounds in Fertilizer y Total number of Pounds Available Nitrogen 6 10 20,000 Phosphorus 8 6 16,400 Potash 6 4 12,000
Use your schools library, the Internet, or some other reference source to find the real-life applications of constrained optimization.
please can you help with the following question with alternative working out thanks a lot
Sketch the feasible region of the program and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution give the objective value for this solution. If an optimal solution does not exist, state why. maximize subject to - 2x1 + x₂ I1 - ₂ ≤ 1, 2x₁ - x₂ ≥ 1, 2x1 + 2x₂ ≥ 4, I1, I₂ 20
1a and 2a please written out
Meatpacking Company produces a hot dog mixture in 1,000-pound batches. The mixture contains two ingredients chicken and beef. The cost per pound of each of these ingredients is as follows : Ingredient Chicken Вef Cost/lb. 165 275 Each batch has the following recipe requirements: At least 500 pounds of chicken At least 200 pounds of beef The ratio of chicken to beef must be at least 2 to 1. The company wants to know the optimal mixture of ingredients that will minimize cost. Formulate a linear programming model for this problem. A. Solve using the steps in Linear Programming Formulation B. Find the coordinates for the graphical analysis
A paper manufacturing company converts wood pulp to writing paper and newsprint. The profit on a unit of writing paper is $500 and the profit on a unit of newsprint is $350. Solve, a. Let x represent the number of units of writing paper produced daily. Let y represent the number of units of newsprint produced daily. Write the objective function that models total daily profit. b. The manufacturer is bound by the following constraints: * Equipment in the factory allows for making at most 200 units of paper (writing paper and newsprint) in a day. * Regular customers require at least 10 units of writingpaper and at least 80 units of newsprint daily. Write a system of inequalities that models these constraints. c. Graph the inequalitiers in part (b) Use only the first quadrant, because x and y must both be positive. (Suggestion: Let each unit along the x- and y-axes represent 20.) d. Evaluate the objective function at each of the three vertices of the graphed region. e. Complete the missing…
To specify that x1 must be at most 75% of the blend of x1, x2, and x3, what constraint should be included in the optimization model?
A television manufacturer makes rear-projection and plasma televisions. The profit per unit is $125 for the rear-projection televisions and $200 for the plasma televisions.a. Let x = the number of rear-projection televisions manufactured in a month and let y = the number of plasma televisions manufactured in a month. Write the objective function that models the total monthly profit.b. The manufacturer is bound by the following constraints:. Equipment in the factory allows for making at most 450 rear-projection televisions in one month.. Equipment in the factory allows for making at most 200 plasma televisions in one month..The cost to the manufacturer per unit is $600 for the rear-projection televisions and $900 for the plasma televisions. Total monthly costs cannot exceed $360,000.Write a system of three inequalities that models these constraints.c.Graph the system of inequalities in part (b).Use only the first quadrant and its boundary, because x and y must both be nonnegative.d.…
For this linear programming problem, formulate the linear programming model. Then, find the optimal solution graphically for the LP with only 2 variables. i.e: Max Z = 500x + 300y Subject to: 4x + 2y <= 60 (1st constraint) 2x + 4y <= 48 (2nd constraint) x, y >= 0 (non-negativity) A television producer designed a program that will include a comedy and advertisements. The advertiser insists on at least 4 minutes of advertising time. The producer insists on not more than 8 minutes of advertisement. The comedian insists on at least 5 minutes of the comedy portion. The total time allotted for the comedy and advertisement cannot exceed one hour. If it has been determined that each minute of advertising attracts 400,000 viewers and each minute of the comedy program attracts 405,000 viewers, how many minutes should be given to each of the comedy and advertisement in order to maximize the number of viewers?
please answer in details and tell the correct answer with explanation within 30 minutes. Its urgent. please help
Hey I was Hoping if i could get some help with this question. Identify The variables X and Y: Find the objective Function: Graph The Constraints: Identify The vertices of the feasible region and their value

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Algebra for College Students

Algebra

ISBN:

9781285195780

Author:

Jerome E. Kaufmann, Karen L. Schwitters

Publisher:

Cengage Learning

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

College Algebra (MindTap Course List)

Algebra

ISBN:

9781305652231

Author:

R. David Gustafson, Jeff Hughes

Publisher:

Cengage Learning

Glencoe Algebra 1, Student Edition, 9780079039897…

Algebra

ISBN:

9780079039897

Author:

Carter

Publisher:

McGraw Hill

Elementary Linear Algebra (MindTap Course List)

Algebra

ISBN:

9781305658004

Author:

Ron Larson

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS