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

Section: Chapter Questions

Problem 1RQ

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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.
Please don't provide handwrittin solution......
8) The following is the optimal tableau for a maximization LP model with thee (s) constraints and all nonnegative variables. The variables x3, x4 and x5 are the slacks associated with the three constraints. Determine the associated optimal objective value in two different ways by using the primal and dual objective functions? Basic X2 Solution 2. I 1 0. DFoas Accessiblity: Investigate
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
A restaurant requires different numbers of full-time employees on different days of the week.Union rules state that each full-time employee must five consecutive days and then two daysoff. The management office wants to meet its daily requirements (Monday: 11, Tuesday: 16,Wednesday: 14, Thursday: 15, Friday: 18, Saturday: 19 and Sunday: 23) using only full-timeemployees. Formulate an LP that the restaurant can use to minimize the number of full timeemployees who must be hired
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-
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Write the equation of the function shown below if it is known that f(0) = -18 25 20+ 15 10+ st ↓
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