Question

Consider the following LP problem:           Max   3X1 + 2X2           s.t. 5X1 + 4X2 £...

Consider the following LP problem:

          Max   3X1 + 2X2

          s.t. 5X1 + 4X2 £ 40

                3X1 + 5X2 £ 30

                3X1 + 3X2 £ 30

                       2X2 £ 10

                X1 ³ 0, X2 ³ 0

(1)   Show each constraint and the feasible region by graphs. Indicate the feasible region clearly.   (5 points)

(2)   Are there any redundant constraints? If so, what constraint(s) is redundant? (2 points)

(3)   Identify the optimal point on your graph. What are the values of X1

      and X2 at the optimal point? What is the optimal value of the

      objective function? (5 points)

(4)   What would be the optimal values of X1 and X2 and the optimal value of the objective function if the objective function is changed to Max 3X1 + 9X2 while all constraints remain unchanged? (5 points)

(5)   Suppose there is one more constraint X1 => 10 in addition to the original problem. What is the optimal solution? (3 points)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Solve The LP problem using the graphic method Z Max=5X1+3X2 Constaint function: 2X1 + 4X2 ≤...
Solve The LP problem using the graphic method Z Max=5X1+3X2 Constaint function: 2X1 + 4X2 ≤ 80 5X1 + 2X2 ≤ 80 X1≥ 0 , X2≥0
max Z = 5x1+3x2+x3 s.t : 2x1+x2+x3 < 6 x1+2x2+x3 < 7 x1, x2, x3 >...
max Z = 5x1+3x2+x3 s.t : 2x1+x2+x3 < 6 x1+2x2+x3 < 7 x1, x2, x3 > 0 Solve the problem. What is the optimal value of the objective function (OF)? Decision variables? Solve the problem. What is the optimal value of the objective function (OF)? Decision variables? (20 points)
Consider the following LP problem: Minimize Cost = 3x1 + 2x2 s.t. 1x1 + 2x2 ≤...
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 What is the optimal solution of this LP? (0,8)(12,0)(4,0)(0,4)(2,3)(0,6)(3,2) I NEED SOLUTION!
Solve The LP problem using the graphic method Z Max=15X1+10X2 Constaint function: 3X1 + 2X2 ≤...
Solve The LP problem using the graphic method Z Max=15X1+10X2 Constaint function: 3X1 + 2X2 ≤ 80 2X1 + 3X2 ≤ 70 X1≥ 0 , X2≥0
Consider the following mixed-integer linear program. Max     3x1 + 4x2 s.t. 4x1 + 7x2 ≤ 28...
Consider the following mixed-integer linear program. Max     3x1 + 4x2 s.t. 4x1 + 7x2 ≤ 28 8x1 + 5x2 ≤ 40 x1, x2 ≥ and x1 integer (c) Find the optimal solution for the mixed-integer linear program. (Round your answers to three decimal places, when necessary.)
Solve The LP problem using the graphic method Z Max=6X1+5X2 Constaint function: X1 + 2X2 ≤...
Solve The LP problem using the graphic method Z Max=6X1+5X2 Constaint function: X1 + 2X2 ≤ 240 3X1 + 2X2 ≤ 300 X1≥ 0 , X2≥0
Consider the following LP Min Z = 4X1+X2 s.t. 3X1+X2=3 4X1+3X2>=6 X1+X2<=4 X1 , X2 >=...
Consider the following LP Min Z = 4X1+X2 s.t. 3X1+X2=3 4X1+3X2>=6 X1+X2<=4 X1 , X2 >= 0 a) Put the problem into standard form, using slack, excess, and artificial variables. b) Identify the initial BV and NBV along with their values. c) Modify the objective function using an M, a large positive number. d) Apply the Big M method to find the optimal solution
Duality Theory: Consider the following LP: max 2x1+2x2+4x3 x1−2x2+2x3≤−1 3x1−2x2+4x3≤−3 x1,x2,x3≤0 Formulate a dual of this...
Duality Theory: Consider the following LP: max 2x1+2x2+4x3 x1−2x2+2x3≤−1 3x1−2x2+4x3≤−3 x1,x2,x3≤0 Formulate a dual of this linear program. Select all the correct objective function and constraints 1. min −y1−3y2 2. min −y1−3y2 3. y1+3y2≤2 4. −2y1−2y2≤2 5. 2y1+4y2≤4 6. y1,y2≤0
Consider the following LP: Max Z=X1+5X2+3X3 s.t. X1+2X2+X3=3 2X1-X2 =4 X1,X2,X3≥0 a.) Write the associated dual...
Consider the following LP: Max Z=X1+5X2+3X3 s.t. X1+2X2+X3=3 2X1-X2 =4 X1,X2,X3≥0 a.) Write the associated dual model b.) Given the information that the optimal basic variables are X1 and X3, determine the associated optimal dual solution.
3) Find the dual of the following LP: Max 4x1 - x2 s.t. 2x1 + 3x2...
3) Find the dual of the following LP: Max 4x1 - x2 s.t. 2x1 + 3x2 ≥ 10 x1 – x2 = 4 0.5x1 + 2x2 ≤ 20 x1 ≥ 0, x2 unconstrained Please provide an excel solution to this problem
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT