(A) Introduce slack, surplus, and artificial variablesand form the modified problem.(B) Write the preliminary simplex tableau for themodified problem and find the initial simplex tableau.(C) Find the optimal solution of the modified problemby applying the simplex method to the initial simplextableau.(D) Find the optimal solution of the original problem,if it exists.Maximizesubject toP = 5x1 + 4x2x1 + x2 ≥3-x1 +5x2 ≤18X1, X2 ≥0(A) Introduce slack, surplus, and artificial variables and form the modified problem.Maximizesubject toP=5x1 +4x2 Mx1 + x2 - + = 3-X1+5x2 += 18X1,X2, S1, S2, a₁≥0

Answered: (A) Introduce slack, surplus, and…

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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An investor has $621,000 to invest in bonds. Bond A yields an average of 8% and the bond B yields 7%. The investor requires that at least 5 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. This can be set up as a linear programming problem. Introduce the decision variables: x= dollars invested in bond Ay= dollars invested in bond B Compute x+y. $ . Round to the nearest cent. Investor Matt has $152,000 to invest in bonds. Bond A yields an average of 9.2% and the bond B yields 8.4%. Matt requires that at least 4 times as much money be invested in bond A as in bond B. You must invest in these bonds to maximize his return. What is the maximum return? $ per year. Round to the nearest cent. Investor Dan has $607,000 to invest in bonds. Bond A yields an average of 8.5% and the bond B yields 8.4%. Dan requires that at least 4 times as much money be invested in bond A as in…
Determine whether the following statement is true or false, and explain why. A surplus variable of a linear programming problem can never have a negative value during the intermediate steps of the simplex method. Choose the correct answer below. O A. The statement is true. A surplus variable always has a positive value during every step of the simplex method, including intermediate steps. B. The statement is false. A surplus variable cannot have a negative value at the beginning or end of the simplex method. It almost always has a negative value during at least some of the intermediate steps. C. The statement is true. A surplus variable can never have a negative value during any step of the simplex method, including intermediate steps. D. The statement is false. A surplus variable cannot have a negative value at the beginning or end of the simplex method. It may have a negative value during an intermediate step.
Solve the linear programming problem using the simplex method. Maximize P = -x₁ + 2x₂ subject to x₁ + x₂ ≤2 -X₁ + 3x₂ ≤18 X₁-4x2 ≤8 X₁, X₂ 20 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The maximum value of P is P= (Simplify your answers.) OB. There is no optimal solution. when x₁ = *** and X₂=

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