Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2...
MAX X Z = 3X1 + 4x2 s.t 2x1 + 2x2 ≤ 8 1x1 + 2x2 ≤ 6 2x2 ≥ 1 please graph with the optimal solution. Then dual price for the first constraint by adding one. Then dual price for the third constraint adding one. Please also graph these with the same graph showing the new optimal solutions Also please show the iso-z lines for the initial problem.
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤ 12 2x1 + 3 x2 = 12 2 x1 + x2 ≥ 8 x1≥ 0, x2 ≥ 0 A) What is the optimal solution of this LP? Give an explanation. (4,0) (2,3) (0,8) (0,4) (0,6) (3,2) (12,0) B)Which of the following statements are correct for a linear programming which is feasible and not unbounded? 1)All of the above. 2)Only extreme points may be optimal....
Consider the following linear program: Max 2X + 3Y s.t. 5X +5Y ≤ 400 -1X+ 1Y ≥ 10 1X + 3Y ≥ 90 X, Y ≥ 0 a. Use the graphical solution procedure to find the optimal solution. b. Conduct a sensitivity analysis to determine the range of optimality for the objective function coefficients X & Y. c. What are the binding constraints? d. If the right-hand-side of the binding constraints are marginally increased, what will be the Dual Value?
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25
Problem 8-02 (Algorithmic) Consider the problem Min 2x2 18X2XY - 18Y58 X 4Y 8 s.t. a. Find the minimum solution to this problem. If required, round your answers to two decimal places. for an optimal solution value of Optimal solution is X Y b. If the right-hand side of the constraint is increased from 8 to 9, how much do you expect the objective function to change? If required, round your answer to two decimal places c. Resolve the problem...
Given the following all-integer linear program: (COMPLETE YOUR SOLUTION IN EXCEL USING SOLVER AND UPLOAD YOUR FILE. BE SURE THAT EACH WORKSHEET IN THE EXCEL FILE CORRESPONDS TO EACH QUESTION BELOW ) Max 15x1 + 2x2 s. t. 7x1 + x2 <= 23 3x1 - x2 <= 5 x1, x2 >= 0 and integer a. Solve the problem (using SOLVER) as an LP, ignoring the integer constraints. What solution is obtained by rounding up fractions greater than or...
Problem 1 (20 pts) Consider the mathematical program max 3x1+x2 +3x3 s.t. 2x1 +x2 + x3 +x2 x1 + 2x2 + 3x3 +2xs 5 2x 2x2 +x3 +3x6-6 Xy X2, X3, X4, Xs, X620 Three feasible solutions ((a) through (c)) are listed below. (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) (c) x Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution. 25 Problem 1 (20 pts) Consider...
Consider the mathematical program max 3x1 x2 +3x3 s.t. 2X1 + X2 + X3 +X4-2 x1 + 2x2 + 3x3 + 2xs 5 2x1 + 2x2 + x3 + 3x6 = 6 Three feasible solutions ((a) through (c)) are listed below. (b) xo) (0.9, 0, 0, 0.2,2.05, 1.4) (c) xo) (0.3, 0.1, 0.4, 0.9, 1.65, 1.6) Please choose one appropriate interior point from the list, and use the Karmarkar's Method at the interior point and determine the optimal solution.
Consider the following LP problem developed at Zafar Malik’s Carbondale, Illinois, optical scanning firm: Maximize profit: = $1x1 + $1x2 Subject to: $2x1 + $1x2 ≤ 100 $1x1 + $2x2 ≤ 100 a. What is the optimal solution to this problem? b. If a technical breakthrough occurred that raised the profit per unit of X1 to $3, would this affect the optimal solution? c. Instead of an increase in the profit coefficient X1 to $3, suppose that profit was overestimated...
Problem needs to be done Excel. 1. Solve the following LP problem. Max Z = 3X1 + 5X2 S.T. 4X1 + 3X2 >= 24 2X1 + 3X2 <= 18 X1, X2 >= 0 a) Solve the Problem b) Identify the reduced costs and interpret each. c) Calculate the range of optimality for each objective coefficient. d) Identify the slacks for the resources and calculate the shadow price for each resource.