Consider the following LP problem. Minimize z = 5x1 + 6x2+7x3, Subject to Constraint 1: 7x1 + 6x2 + 4x3 >= 50, Constraint 2: 10x1 + 13x2 + 14x3 >=150, Constraint 3: x1, x2, x3 >=0, where x1, x2, and x3 represent the decisionvariables. Solve the LP problem to answer the following questions. a-1. What are the values of x1, x2, and x3 at the optimal solution? Note: Round your answers to 2 decimal places. a-2. What is the minimum value of z? Note: Round your answers to 2decimal places. b. Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constraints is "Non-Binding" enter surplus value to 2 decimal places or leave cells blank. c. Report the values andranges of feasibility of the shadow price of each binding constraint. Interpret the results. Note: Round your answers to 2 decimal places. d. What is the range of optimality for the three objective function coefficients? Interpret the results. Note: Roundyour answers to 2 decimal places.

This linear programming (LP) problem aims to minimize the value of a function (z) considering…

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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Solve the following LP using the simplex method: Note: The constraint with the "=" sign in the simplex iteration is added with an artificial variable, so that it becomes 3x1 + x2 + A1= 3
Group B 10 Money manager Boris Milkem deals with French currency (the franc) and American currency (the dollar). At 12 midnight, he can buy francs by paying .25 dollars per franc and dollars by paying 3 francs per dollar. Let x, = number of dollars bought (by paying francs) and x2 = number of francs bought (by paying dollars). Assume that both types of transactions take place simultaneously, and the only constraint is that at 12:01 A.M. Boris must have a nonnegative number of francs and dollars. a Formulate an LP that enables Boris to maximize the number of dollars he has after all transactions are completed. b Graphically solve the LP and comment on the answer.
A company produces two types of drills, a cordless model and a corded model. The cordless model requires 3 hours, and the corded-type drill requires 1 hours to make. The company has 180 work hours per day for manufacturing. The factory has space for storage of 140 drills per day. Let z = the number of cordless drills produced per day and y = the number of corded drills produced per day. Write the system of inequalities for these constraints: Assembly: 3x + y Storage: x+y 250+ 240 230- 220- 210- 200 Graph the feasible region for this system of inequalities. Note: To get the correct feasible region, you need to also include the non-negative constraints on your graph (≥0 and y ≥ 0). These will give you boundary lines on the x-axis and y-axis. 190 180 170- 160- 150 140 130 120 110- 100 90- 688888888 80 70 60- 50- 40- 30 20- 10 <180 <140 Clear All Draw: 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250
1- Convert the following constraints and objective function into the standard form for use in the simplex: Max Profit: 40X, + 20X₂ Sto 2X; +3X2 ≤ 120 X₁ +2X₂ ≥100 X₁, X₂ 20
Verify that in the example to the right, the same result isobtained if the constraint x + y = 20 is used to eliminate x rather than y.
Consider the following minimum problem: Minimize: C= 2x1 +10x2 + 8x3 Subject to the constraints: X2+2x3 2 8 -X1+2x2 +2x3 2 4* |지 20 x2 20 x3 20 Write the dual problem for the above minimum problem by selecting the appropriate number for each blank box shown below (Do not solve the dual problem). P= (Select) yi+ [ Select) 2 + 4y ( Select) Y1-Select ] |Select 1 +y2+ [Select] S 10 y+( Select ) 2+ ( Select ) 20 2 20 ys 20 Question 4
12
Consider the following problem. Maximize subject to and ee0 X₁ + 3x₂ + 4x3 ≤ 30 x₂ + 4x₂ X3 ≤ 10 x₁ ≥ 0, x₂ = 0, X3 ≥ 0. Using slack variables x4 and x5 for the respective constraints, the simplex method yields the following final set of equations: Z = 2x₁ + 7x₂ - 3x3, Z + x₂ + x3 X₂ + 5x3 + x₂ x₂ + 4x₂ X3 + 2x5 = 20 X5 = 20 x₂ = 10. - + (a) Use sensitivity analysis to determine the allowable range for c₁1 (b) Use sensitivity analysis to determine the allowable range for C3
Need only a handwritten solution only (not a typed one).
Solve the linear programming problem. Minimize z = 10x, + 16x, + 20x,, subject to Зх, + х, + 6х, 29 X; + x, 2 9 4х, + х, 2 12 x, 2 0, x, 2 0, x, 2 0 by applying the steps of simplex method of the dual problem shown in Section 6-3 of the textbook.
Solve the following problem using artificial variables. Maximize z = 3x, + 2x2 subject to the constraints x, + x2 = 80, 4x, + 2x, 2 120, and 5x, + 2x2<300, with x, 0, X2 2 0. The maximum is z = when x1 and x2 %3D (Simplify your answers.)
A LP model is given as Max z = 3x1+ 2x2 Subj to 2x1 + 2x2 0 Obtain the dual of the model. Use the variables y1, Y2, Y3, · . . Objective function: Min w= Constraint 1: Constraint 2: With: >0

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