6:18Snapchatbartleby.com1... / Q&A LIb...Linear programming proble...18 of 30 questions leftuntil 10/18/19estionSolve the linear programming problem by the method of corners.C 3x 4yMinimizey 42y 30х + Зу 2 30x2 0, у 2 0subject to 4x +2х +at (x, y)The minimum is C=ted Probability Q&Aanswers to questions asked ShowQ&Audent like youLL

The corner points are the vertices of the feasible region. First draw the feasible region of the…

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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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The following linear programming problem will be used to answer this question AND the next one:Minimize C = 3x + 4ysubject to2x + y ≥ 100x + 3y ≥ 120x ≥ 0, y ≥ 0Which of the following statements is true? A. The feasible region is unbounded, and a corner point is (120, 0). B. The feasible region is bounded, and a corner point is (36, 28). C. The feasible region is bounded, and a corner point is (0, 100). D. The feasible region is unbounded, and a corner point is (0, 40). E. The feasible region is unbounded, and a corner point is (50, 0).
Solve the linear programming problem.Minimize Z = 42x + 10ysubject to2x + 2y ≥ 80x + 6y ≥ 200x, y ≥ 0
Consider the following integer linear programming problem Max Z = 3x1 + 2x2 Subject to: 3x1 + 5x2 ≤ 30 4x1 + 2x2 ≤ 28 x1 ≤ 8 x1 , x2 ≥ 0 and integer The solution to the Linear programming relaxation is: x1 = 5.714, x2 = 2.571. What is the optimal solution to the integer linear programming problem?
We found that the linear programming problem was:Maximize P = 90x+100ySubject to 50x+20y ≤ 4,00075x+150y ≤ 15,000x ≥ 0, y ≥ 0
Let’s solve Example 2 from Section 3.1. We found that the linear programming problem was:Minimize C = 44,000x+54,000ySubject to 60x+40y ≥ 24096x+160y ≥ 672x ≥ 0, y ≥ 0
Consider the following linear programming problem: Minimize 20X + 30YSubject to: 2X + 4Y ≤ 800 6X + 3Y ≥ 120 X, Y ≥ 0 What is the optimum solution to this problem (X,Y)?
Hypertension A national study found that treating people appropriately for high blood pressure reduced their overall mortality by 20%. Treating people adequately for hypertension has been dif- ficult because it is estimated that 50% of hypertensives do not know they have high blood pressure, 50% of those who do know are inadequately treated by their physicians, and 50% who are appropriately treated fail to follow this treat- ment by taking the right number of pills. 1 If the preceding 50% rates were each reduced to 40% by a massive education program, then what effect would this change have on the overall mortality rate among true hypertensives; that is, would the mortality rate decrease and, if so, what percentage of deaths among hypertensives could be prevented by the education program?
Show that the linear programming problem is unbounded.
2. identify the feasible region and optimal solution for the linear program max z =2x1 + 3x2 s.t 1x1 + 2x2 < 6 5x1 + 3x2 < 15 x1, x2 > 0
Consider the following linear program : z = 6x1 + 6x2 + 10x3 → min s.t. 4x1 + 3x2 + 2x3 ≥ 16 x1 + 2x2 + 5x3 ≥ 16 x1, x2, x3 ≥ 0 a) a) Build the dual problem corresponding to the given problem! b) Solve the dual problem graphically! Determine the exact coordinates by computing the intersection point of two appropriate lines! c) Conclude for the solution (objective and variables) of the primal problem by using the complementary slackness conditions.
Consider the following linear programming problem Minimize Z=5X1+6X2+3X3 Subject to 5x1+5x2+3x3>=50 x1+x2-x3=20 7X1+6X2-9X3>=30 5x1+5x2+5x3>=35 2x1+4x2-15x3>=10 12x1+10x2>=90 x2-10x3>=20 X1, X2, X3 >=0 In an Excel workbook, solve the problem by using the Solver. Generate the Solver sensitivity and answer reports. In this Word document, write the mathematical formulation of the dual problem. Generate a sensitivity report of the dual problem. Solve the dual problem in another sheet of the same Excel file. In this Word document, describe whether the solution of the dual problem offers a computational advantage and explain why. Submit the Excel workbook as a separate attachment.
2. Consider the linear program below and the optimal simplex tableau.Maximize 2x1+6x2+8x3Subject to x1+x2-2x3 ≤ 10-x1+x2+2x3 ≤ 20x1+x2+x3 = 10xi ≥ 0, i = 1, 2, 3. x1 x2 x3 x4 x5 y1 RHS BV0 2 0 1 1 0 30 x40 2/3 1 0 1/31/3 10 x31 1/3 0 0 -1/32/3 0 x10 0 0 0 2 M+4 80 ⇐ OBJHere y1 is artificial variable in constraint 3.(a) Introduce a new variable x6 with cost coefficient 10 and constraint coefficients 1, 1, 1 and compute the new optimal solution, if any.(b) Delete variable x3 from the given tableau and obtain the new optimal solution, if exists.

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