Question 3 Solve the following linear program: Max 3x+2y s.t. 2x+2y <8 A 3x+2y < 12...
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?
Consider the following integer program Max 2x+3y s.t 6x+7y23 x-y<12 xy0 x,y: integer Let V1 denote the optimal objective value of the above optimization problem. Let V2 denote the optimal objective value of the optimization problem obtained by dropping "x,y: integer" constraint. Similarly, let V3 denote the optimal objective value of the optimization problem obtained by dropping "x-y<-12" constraint which one of the following statements is correct? a. V2 V1 and V3<-V1 b. V1 V2 and V1<-V3 c. V2V1 but...
For the linear program Max 3A+2B s.t. A+B>=4 3A+4B<=24 A>=2 A-B<=0 A, B>=0 a. Write the problem in standard form. b. Solve the problem. c. What are the values of the slack and surplus variables at the optimal solution?
Solve the following linear equations by graphical method. 2x - y = 1 3x + 2y = 4
For the linear program Max 3 A + 3 B s.t. A + 2B ≤ 8 5A + 3B ≤ 15 A, B ≥ 0 Draw graph that identifies the optimal solution. What is the value of the objective function at the optimal solution?
Question 4 (3 points) Set up and solve the following simple linear optimization model: MAX: 14.9 x + 23.8 y subject to: 2x + 2y = 20 3x 2 17 5x + 1y s 78 x.y 20 What is the value of the objective function at the optimal solution? Round your answer to one decimal place. Your Answer: Answer Question 5 (8 points) -
1. Transform the following linear program into a MAX and in standard form: (DO NOT SOLVE) min z = -2x, + 3x, st. *; -3x, + 2x, S3 - x + 2x 22 *; urs, x, 20, x, 20
Solve the following linear systems of equations by Gaussian elimination. 3x+3z=0 2x+2y=2 3y+3z=3
1254 6B use Cramer's rule to solve linear system [ 3x+2y+43 = 17... (1) 2x+4y-32=8 (2) 44. By+22=-1 (3)
1. (20 pts.) Consider the following linear program: max 4x4 +xz+5x3 +3x4 s.t. *1 -X2 -X3 +3X, 51 5x +xz+3X3 +8X555 -X2 +2x2+3x3 -5x53 It is claimed that the solution x* = (0,14,0,5) is an optimal solution to the problem. Give a proof of the claim. Do not use the simplex method to solve this problem.