**Problem 2**Consider the following Linear Programming (LP) problem:Maximize $ Z = x_1 + x_2 $Subject to:- $ x_1 + x_2 \leq 3 $- $ x_1 - 2x_2 \geq 0 $- $ x_1, x_2 \geq 0 $a. Solve the problem graphically: clearly mark each constraint, the feasible region, the iso-profit line, and the optimal solution on the graph.**Graph Explanation:**- The graph is a standard coordinate plane divided into a grid for plotting points.- Plot each constraint line: - $ x_1 + x_2 = 3 $ as a straight line with intercepts at (3,0) and (0,3). - $ x_1 = 2x_2 $ as a line through the origin (0,0) with a slope of 1/2. - The axes $ x_1 = 0 $ and $ x_2 = 0 $ represent the non-negativity constraints.- Shade the feasible region determined by these constraints.- Draw an iso-profit line parallel to $ x_1 + x_2 = Z $, moving outward to identify the optimal point.- Mark the optimal solution on the graph where the iso-profit line is tangent to the feasible region.

Answered: Image /qna-images/answer/d5d01485-c123-403d-b945-118f4a467fd5.jpg

Answered: Consider the following LP: Max Z = x1 +…

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...

See similar textbooks

Similar questions

Find the maximum and minimum values of the objective function p = 5x – 6y under the constraints y – 2x 2 3y + x > 3. Sketch the feasible region and mark all corner points.
Estimate a range for the optimal objective value for the following LPs: *(a) Minimize z = 5x₁ + 2x₂ subject to (b) Maximize z subject to x₁ + 5x₂ + 3x3 X₁ X₂ ≥ 3 2x₁ + 3x₂ = 5 X1, X₂ ≥ 0 x₁ + 2x₂ + x3 = 30 2x₁ - x₂ = 40 X1, X2, X3 ≥ 0
Bugs Bunny and Daffy Duck are contestants on a game show called Split or Steal. On the show, Bugs and Daffy have to pick one of two cards and decide to split the prize money of $100,000 or steal it from the other contestant. The decisions are made simultaneously so neither player knows what the other will do. The table below represents the result of the contestants’ choices. See attached What should a rational player do in this game? Is this a zero-sum game?
Solve the following linear programming problem graphically: Maximize Z=3X+5Y Subject to: 4X+4Y ≤48 C1 1X+2Y ≤20 C2 Y ≥2 C3 X, Y ≥0 Part 2 1) Using the line drawing tool, plot constraint C1 by picking two endpoints for the line. 2) Using the point drawing tool, plot the corner points which define the feasible region. The optimal solution is X= ____ and Y= _______ ( round your responses to whole numbers) Maximum Profit is $ _____ ( round your responses to whole numbers)
Using Excel Solve the following LP Maximize $4x + $5y Subject to 2x + 3y ≤ 20 (labor, in hours) 6x + 6y ≤ 36 (materials, in pounds) 4x + 4y ≤ 40 (storage, in square feet) x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material? c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor?
b) The figure below presents an unbounded feasible region of a five constrained LP problem. 10- |(0, 6) 6. (1, 4) 4 (3, 2) 2+ (9, 0) 8 10 i. Write down in terms of x and y the inequalities that represent these constraints. ii. If the objective function is Z = 0.12x + 0.15y, determine the optimal solution to this problem (show the movement of the isocost line). ii. Identify the binding and non-binding constraints.
Answer the next TWO (2) questions using the following linear programming problem and the corresponding graphical solution: Max subject to Z=30 x₁ +20 x₂ 2 x₁ + 2x₂ ≤8 8 x₁ +4x2 ≤24 X₂ 2 (constraint I) (constraint II) 13. What is the upper bound of the sensitivity range for the coefficient of x₁ in the objective function? a. 60 b. 10 c. 40 d. 20 14. What is the upper bound of the sensitivity range for the Right-Hand Side (RHS) of constraint I? a. 8 b. 12 c. 4 d. 6
Variable Cells Model Variable Constraints E S D Constraint Number 1 E 2 3 S D S D Name Economy Models Standard Models Deluxe Models Name Total Profit: $ Fan Motors Cooling Coils Manufacturing Time Optimal Solution Constraints Fan motors Cooling coils Final Value 80.000 120.000 0.000 Final Value 200.000 320.000 2080.000 a. Identify the range of optimality for each objective function coefficient. If there is no lower or upper limit, then enter the text "NA" as your answer. If required, round your answers to one decimal place. Objective Coefficient Range Variable lower limit upper limit E Reduced Cost 0.000 0.000 -24.000 Manufacturing time. AUTO Shadow Price 31.000 32.000 0.000 Right-Hand-Side-Range lower limit upper limit Objective Coefficient 63.000 95.000 135.000 b. Suppose the profit for the economy model is increased by $6 per unit, the profit for the standard model is decreased by $2 per unit, and the profit for the deluxe model is increased by $4 per unit. What will the new optimal…

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Operations Management

ISBN:

9781259667473

Author:

William J Stevenson

Publisher:

McGraw-Hill Education

Operations and Supply Chain Management (Mcgraw-hi…

Operations Management

ISBN:

9781259666100

Author:

F. Robert Jacobs, Richard B Chase

Publisher:

McGraw-Hill Education

Business in Action

Operations Management

ISBN:

9780135198100

Author:

BOVEE

Publisher:

PEARSON CO

Purchasing and Supply Chain Management

Operations Management

ISBN:

9781285869681

Author:

Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson

Publisher:

Cengage Learning

Production and Operations Analysis, Seventh Editi…

Operations Management

ISBN:

9781478623069

Author:

Steven Nahmias, Tava Lennon Olsen

Publisher:

Waveland Press, Inc.

SEE MORE TEXTBOOKS

Consider the following LP: Max Z = x1 + x2 s.t. X1 + x2 < 3 X1 – 2x2 >0 X1, X2 2 0 a. Solve the problem graphically: clearly mark each constraint, the feasible region, the iso-profit line and the optimal solution on the graph.