Question: 3. Please follow these steps to do sensitivity analysis for the LP: max z = 10x1 + 2x2 s.t. 2x1 + x2 0 Its optimal

3. Please follow these steps to do sensitivity

3. Please follow these steps to do sensitivity analysis for the LP: max z = 10x1 + 2x2 s.t. 2x1 + x2 0 Its optimal solution is x1 = 3, x2 = 0,= 0,52 = 6 and z = 30. The basis for this optimal solution is BV = {x1, S2}, NBV = {X2,51}, where S1,S2 are slack variables for first and second constraint, respectively. 3.1 (2 points) Write the standard form. 3.2 (8 points) Write all related matrices or vectors XBv, XNBV, CBV, Cnby, B, N, b and also compute B-1. 3.3 (7 points) Let cu be the coefficient for x in the objective function. Currently, C1 = 10. In what range if c changes (all other parameters stay the same), the current basis remains optimal? 3.4 (4 points) Based on the problem 3.3, if c = 9, what are the optimal solution for decision variables, and optimal objective value? 3.5 (6 points) Let by be the RHS of 1st constraint. Currently, b2 = 6. In what range if b changes (all other parameters stay the same), the current basis remains optimal? 3.6 (4 points) What are the shadow prices for the first two constraints of the original LP problem? 3.7 (4 points) Based on the problem 3.5 and the shadow price from problem 3.6, if b2 = 8, what are the optimal solution for decision variables and optimal objective value? 3. Please follow these steps to do sensitivity analysis for the LP: max z = 10x1 + 2x2 s.t. 2x1 + x2 0 Its optimal solution is x1 = 3, x2 = 0,= 0,52 = 6 and z = 30. The basis for this optimal solution is BV = {x1, S2}, NBV = {X2,51}, where S1,S2 are slack variables for first and second constraint, respectively. 3.1 (2 points) Write the standard form. 3.2 (8 points) Write all related matrices or vectors XBv, XNBV, CBV, Cnby, B, N, b and also compute B-1. 3.3 (7 points) Let cu be the coefficient for x in the objective function. Currently, C1 = 10. In what range if c changes (all other parameters stay the same), the current basis remains optimal? 3.4 (4 points) Based on the problem 3.3, if c = 9, what are the optimal solution for decision variables, and optimal objective value? 3.5 (6 points) Let by be the RHS of 1st constraint. Currently, b2 = 6. In what range if b changes (all other parameters stay the same), the current basis remains optimal? 3.6 (4 points) What are the shadow prices for the first two constraints of the original LP problem? 3.7 (4 points) Based on the problem 3.5 and the shadow price from problem 3.6, if b2 = 8, what are the optimal solution for decision variables and optimal objective value

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related General Management Questions!

2. Please follow these steps to do sensitivity analysis for the LP: max z = 40x; + 100x2 s.t. X: + 2x2 3 40 4x, +3x2 S 120 X4,X, 20 Its optimal solution is x1 = 0.x2 = 20,51 = 0.5, = 60 and z = 2000....

(a) Consider the LP problem in Figure QP2.1 and refer to the Solver sensitivity report in Figure QP2.2. Max z = 3x1 + 2x2 s.t. 2x1 + X2 5 4 (C1) X1 + 3x2 54 (C2) X1 53 (C3) x1 20 (C4) X2 20 (C5)...

(a) Let x1 , 22 represent decision variables. Which of the following is a linear constraint? (a) 0.5x1 + 22 5 1 (b) 212 2 4 (d) (ax1 + 1)2 + 23 2 1 O (d) O (b) O (a) O (c)A stall owner sells two...

Sude makes necklaces and sell them to jewelry shops. Right now she is able to produce two different types of necklaces using brass and steel. A type 1 necklace requires 2 units of brass and 4 units...

please solve X Photos - LP problem.jpeg Edit & Create v See all photos Add to Q5. (Sensitivity Analysis: Adding a new variable) (2 marks) Suppose that we have the following LP model: max z = 3x1 +...

Problem 1: Set up the initial simplex tableau and work through one iteration (in TABULAR form). Show the values of x 1 , x 2 and z after one iteration. Maximize Z = 3 x 1 + 2 x 2 , Subject to x 1 4 x...

. Solve the given LP problem on the right by using graphical solution method. a- Find the optimal solution. b- Find the optimality range for the changes in the objective coefficient c2. c- Find the...

7 The following questions refer to the Giapetto problem (Section 3.1). Giapettos LP was a Show that as long as soldiers (x1) contribute between $2 and $4 to profit, the current basis remains optimal....

Answer this using both graphical analysis and MS Excel. Radioco manufactures two types of radios. You may assume they can produce partial radios. The only scarce resource that is needed to produce...

Problem 4: Consider the graphical representation of the following LP problem in which X1 and X2 are the number of desks and file cabinets produced per week, respectively Max z= 3X1 + 2X2 St. 2X1 + X2...

What type of knowledge must an accountant possess about the entity in order to perform a compilation engagement? A review engagement?

4. (12 points) (a) Draw a picture of a binary search tree if nodes with the given keys are inserted in this order 25 47 73 36 29 14 42 20 8 23 81 75 (b) Draw the complete resulting binary search tree...

In general, people who retire early miss their work colleagues and soon return to work feel that they have made the right decision if they have enough money quickly abandon their fantasies of taking...

atch the compensation objectives with their meanings. Efficiency Efficiency drop zone empty. Fairness Fairness drop zone empty. Compliance Compliance drop zone empty. Improving performance and...