Consider the following LP problem developed at Zafar Malik's Carbondale, Illinois,optical scanning firm:MaximizeZ = 1X₁ + 1X₂Subject to:2X₁ + 1X₂ ≤ 100(C₁)1X₁ + 2X₂ ≤ 100(C₂)X₁, X₂20On the graph on right, constraints C, and C₂ have been plotted.a) Using the point drawing tool, plot all the corner points for the feasible area.The optimum solution is:X₁ =(round your response to two decimal places).(round your response to two decimal places).X₂ =Optimal solution value Z =(round your response to two decimal places).b) If a technical breakthrough occurred that raised the profit per unit of X₁ to $3,due to this change, the optimal solutionAs a result of the technical breakthrough, the optimum solution is:X₁ =(round your response to two decimal places).(round your response to two decimal places).x₂ =1Optimal solution value Z = (round your response to two decimal places).c) If the impact of technical breakthrough was incorrectly determined and insteadof X₁ profit coefficient increasing to $3 it only increases to $1.25. As a result ofthis correction, the optimal solution found originally

Answered: Consider the following LP problem…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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4.). Referring back to question 3. Determine the five vertices of the feasible region, given theconstraints. (You may use Desmos to help with graphing!)Constraints (for this linear programming problem):2x + 6y ≤ 30x ≤ 9y ≤ 3x ≥ 0y ≥ 0 Draw or insert a picture of your graph from desmos here: Answer Choices(select ALL answers below thatare vertices of the feasible region) A. (0, 0) F. (9, 2)B. (9, 3) G. (9, 3)C. (0, 3) H. (0, 9)D. (0, 5) I. (3, 6)E. (6, 3) J. (9, 0)
In the problem, find the miimum value of z = 4x + 5y, subject to the following constraints: 2x+y≤6; x≥0; y ≥0; x+y≤5 (1,-4) is a vertex of the feasible region. True or False
Consider the following LP model and it is graphical solution to answer questions from a) to g). Maximize z= 4x,+5x2 Subject to: X:5 .(1) 2x:+X;512 ..(2) X,+2x;s12 ..(3) X1, X220.. .(4) 12 11 10 D A *9 10 11 12 n a) What is the optimal solution x1, X2 and z? b) Determine the optimality range of the objective function coefficient c1. c) Determine the feasibility range of the right-hand side for constraint 1, 2 and 3. d) How many basic feasible solutions in this problem? e) Is there any binding constraint(s)? f) Dose any constraint has a slack? which one and by how much? g) Dose any constraint has a surplus? which one and by how much?
1) Consider the following linear programming model.Max 3x + ys.t 2x + 4y ≤ 22-x + 4y ≤ 104x - 2y ≤ 14x - 3y ≤ 1x, y≥ 0Provide answers to the following questions using the graphical solution method (Note: This problem must not be solved by Excel Solver).a. Draw the correct graph and show the feasible region. b. What are the extreme points? c. Which point in the feasible region is optimal and what is the valueof the objective function at that point? d. Which constraints are binding and explain why? e. Calculate the slack/surplus for each constraint(s)? 2) Consider the following linear programming problem:Max 5x + 7ys.t 2x + y ≥ 3-x + 5y ≥ 42x - 3y ≤ 63x + 2y ≤ 353/7x + y ≤ 10x, y ≥ 0 a. Solve this problem using the graphical solution procedure. b. Compute the range of optimality for the objective functioncoefficient of x. c. Compute the range of optimality for the objective functioncoefficient of y.
2. Show that the feasible set constrained by the inequalities x > 0, y > 0, 2x+5y < 3, –3x+8y < -5 is empty.
List the corner points for the following collection of constraints of a linear programming problem. x ≤ 13 4x + 6y224 X20 y20 a. (0,4), (6, 0), (13,0) b. (0, 0), (6, 0), (0, 13) c. (0, 0), (0, 4), (13,0) d. (0,4), (0, 24), (13, 0) e. (0, 0), (6, 0), (13,0) O O
Consider the following maximization problem. Maximize subject to the constraints 5x1 I1 201 P = 10x₁ + x₂ - 5x3 x₁ ≥ 0 I₂ +9x3 90 15x2 + 3x3 0 T3 > 0 82 Introduce slack variables and set up the initial tableau below. Keep the constraints in the same order as above, and do not rescale them. P X3 81 I1 X2 83 RHS
2. Graph the ff: in one cartesian plane and find the feasible region(select darkest color for region of the set of solutions) Constraints: 4 x-3y ≤ 1 3x+2y2l ysl x20 } 3. Referring to problem no. 2, find the minimum and maximum values of the objective function: Z=2x-y
min x1 + x2 s.t. 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1, x2 ≥ 0 For the LP problem above, which are the binding constraints? 3x1 + 2x2 ≥ 36 3x1 + 4x2 ≥ 48 x1 ≥ 0 x2 ≥ 0
Given the following linear problem Minimize z = 5x1 + 2x2 + 6x3, subject to: 4X1 + 2x₂ + x3 ≥ 12 3x1 + 2x2 + 3x3 ≤18 X1 + 3x₂ + 4x3 ≤ 13 x ≥ 0, y ≥ 0 a.) Rewrite the problem as a standard maximum problem by modifying constraints as necessary. Clearly identify your final problem. b.) Set up the initial simplex tableau. c.) Your initial solution may be infeasible. Circle a possible pivot element in the tableau for Phase I of the simplex method. Explain your choice, but you do not need to perform the pivot.
5. Consider the following linear programming problem: Maximize: P=12x₁ +10x₂ subject to: 5x₁ +3x₂ ≤ 15 x₁ + x₂ ≤4 x ≥ 0, x₂ ≥0 a) Is the linear programming problem in standard form? YES b) Find the feasible region by graphing. Q Search PN-
Maximize R = 2x + 3ySubject to:2x – y <= 10 (constraint 1)x + 3y <= 6 (constraint 2)x,y ≥ 0 1. Does the graph of constraint 1 pass through (0,0)? 2. Does the graph of constraint 2 pass through (1,1)? 3. How many corner points can be identified from the graph of LP model? 4. What values of x and y will maximize R? 5. What is the maximized value of R?

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