Problem 1 Suppose we have created a simplex tableau for a linear program (assuming it is amaximization problem) that looks like the following:Row012342 x11 -20X2 X30 00 1 0000 -1 0 0X4 X5 x6 rhs1 080 0 00 1 0 01010 12400 31 0 1 0 0 3110 2(a) Based on the current tableau, write down the corresponding basic feasible solution.(b) The current tableau is clearly not optimal. To proceed to the next step, which variable willbe chosen as the entering variable and which variable will be chosen as the leaving variable?(c) Write down the tableau that results from performing one simplex pivot/iteration basedon your choice in part (b). Show your step-by-step work.(d) Is the solution indicated by your simplex tableau optimal after you finish part (c)? If so, writedown the optimal solution and the optimal objective value. If not, identify the next enteringvariable and leaving variable.

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Answered: Problem 1 Suppose we have created a…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Question 20 Use the simplex method to solve the linear programming problem. Maximize z = 3x₁ + 2x2 subject to: 2x1 + 3x2 ≤ 4 4x1 + 2x2 ≤ 12 with X₁ ≥ 0, X₂ ≥ 0 Maximum is 9 when x1 = 3, x2 = 0 Maximum is 12 when x1 = 2, x2 = 3 Maximum is 4 when x1 = 0, x2 = 2 Maximum is 6 when x₁ = 2, x2 = 0
QUESTION 1 The following is a linear Programming problem: Maximize AZ = 68X+51 y subject to the constraints: x+y<35 3x + 2y < 75 x20, y 20 Solve the problem graphically and calculate the Z value of at the optimal solution ( only Write the numeric value of Z in the answer box)
Question 7 Classify the nature of this linear program. Assume all the variables are non-negative. Min-2X + Y subject to 3X-Y 22 -X+ 2Y ≤ 10 Y ≤5
Problem 1: Solve Using Linear Programming •BIG company can advertise on three different websites-Yahoo, MSN and Facebook. •Cost and exposure of each advertisement on these sites are given below: BIG needs to make sure they are reaching at least 100,000 viewers through these ads while keeping their cost to the minimum. There are few other things BIG marketing executives need to keep in mind while planning such as BIG needs to have at least two ads on each one of the websites. Moreover, BIG needs to reach at least 30, 000 people through Yahoo and MSN On the other hand, BIG does not want to have more than 200 ads on Facebook and the number of ads on Facebook needs to be at least 8% of the total ads.
Question#4:Formulate the linear programming problem Problem Statement: A company having two items/products namely P-1 and P-2 with selling prices of 25 and 20respectively. The company has 1800 units of resources availableevery dayto produce these items. An item P-1 requires 20 units of resources and P-2 needs 12 units of resources. The production time for both of these items is 4 minutes and the company gets total of 480 minutes working every day.The problem is, what should be the production quantity for each of these itemsto maximize the company’s profits?note: I am not feeling okay, please help me do my assignment kindly solve it I will be thankfull to you forever <3
For the linear programming problem to the right, (a) Set up the simplex tableau. (b) Determine the particular solution corresponding to the initial tableau (a) Set up the simplex tableau 8 1 0 1 1 0 1 0 0 0 0 1 10 W 0 0 1 0 (b) Determine the particular solution corresponding to the initial tableau x=y=2-u-113, v-w-M=0. 0 0 0 0 1 218 113 Maximize x + 5y-7z subject to the listed constraints. x+y+z=113 7x +x≤218 8x+14y $113 x20, y20, 220
Question 4 Consider the following nonlinear programming problem. Maximize Subject to and f(x₁, x₂) = x1/² x 1/² 1/2 1/2 4x₁ + 2x₂ ≤ 10 X₁ > 0, x₂ > 0 (a) Determine whether the problem is a convex programming problem. (b) Write down the KKT conditions for this problem. (c) Determine a possible solution to the problem.
The initial tableau of a linear programming problem is given. Use the simplex method to solve the problem X₂ X3 S₁ 2 4 1 2 0 0 X₁ 1 3 -5 3 1 -1 $₂ 0 1 0 Z 0 0 11 30 www. The maximum is when x₁ = x₂ = x3 = $₁ (Type integers or simplified fractions.) and $₂ =
Problem #3 D, E,F
QUESTION 2 In a linear programming problem, the objective function always needs to be minimized. True False
1. Give the dual of each of the following linear programs: (b) minimize 3x₁ +7x3 + 9x₁ subject to -₁ + 3x₂ - 3 2x1 +52 +8x3 +974 ≥ 1, 10x₁ < -12, x₁ + 4x₂ + 8x32 -4, I1, I₂ ≥ 0, X3 ≤ 0, T4 unrestricted
10

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