PART4 Consider the following linear programming problem and its optimal final tableau shown below. RH Max Z
Fantastic news! We've Found the answer you've been seeking!
Question:
PART4
Transcribed Image Text:
Consider the following linear programming problem and its optimal final tableau shown below. RH Max Z = 2x1 + x2 X3 Row X1 X2 X3 X4 X5 S Subject to X1 + 2x2 + x3 < 8 1 3 3 2 16 -X1 + x2 -2x3 < 4 1 1 2 1 1 8 X1 X1, X2, X3 2 0 2 3 -1 1 12 X5 (a) Write the dual problem and find the optimal dual variables from the foregoing tableau. [5 points] (b) Suppose that you do not know the optimal solution to the primal. Using the complementary slackness and optimal dual solution obtained in part (a), find the optimal solution to the primal. [10 points] (c) Using sensitivity analysis, find the new optimal solution if the coefficient of x2 in the objective function is changed from 1 to 6. [5 points] (d) Suppose that the coefficient of x2 in the first constraint is changed from +2 to -. Using sensitivity, find new optimal solution. [5 points] (e) Suppose that a new constraint x2 + x3 = 3 is added to the problem. Using sensitivity, find the new optimal solution. [10 points] (f) If you were to choose between increasing the right-hand-side of the first and second constraints, which one would you choose? Why? What is the effect of this increase on the optimal value of the objective function? [5 points] (g) Suppose that a new activity x6 is proposed with unit return 4 and consumption vector a6 = (1, 2)'. Find the new optimal solution. [5 points] Consider the following linear programming problem and its optimal final tableau shown below. RH Max Z = 2x1 + x2 X3 Row X1 X2 X3 X4 X5 S Subject to X1 + 2x2 + x3 < 8 1 3 3 2 16 -X1 + x2 -2x3 < 4 1 1 2 1 1 8 X1 X1, X2, X3 2 0 2 3 -1 1 12 X5 (a) Write the dual problem and find the optimal dual variables from the foregoing tableau. [5 points] (b) Suppose that you do not know the optimal solution to the primal. Using the complementary slackness and optimal dual solution obtained in part (a), find the optimal solution to the primal. [10 points] (c) Using sensitivity analysis, find the new optimal solution if the coefficient of x2 in the objective function is changed from 1 to 6. [5 points] (d) Suppose that the coefficient of x2 in the first constraint is changed from +2 to -. Using sensitivity, find new optimal solution. [5 points] (e) Suppose that a new constraint x2 + x3 = 3 is added to the problem. Using sensitivity, find the new optimal solution. [10 points] (f) If you were to choose between increasing the right-hand-side of the first and second constraints, which one would you choose? Why? What is the effect of this increase on the optimal value of the objective function? [5 points] (g) Suppose that a new activity x6 is proposed with unit return 4 and consumption vector a6 = (1, 2)'. Find the new optimal solution. [5 points]
Expert Answer:
Related Book For
Finite Mathematics and Its Applications
ISBN: 978-0134768632
12th edition
Authors: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair
Posted Date:
Students also viewed these organizational behavior questions
-
Xeno Co. incurred the following transactions concerning its machinery: Jan 1, 2021Purchased a machine for $60,000 cash, and also paid $3,000 cash to have it installed. Estimated useful life is 10...
-
Consider a steady, laminar, fully developed incompressible flow between two infinite parallel plates separated by a distance 2h . The top plate moves with a velocity V0. Derive an expression for the...
-
Draft an email to the relevant people in the organization to gain agreement for the policy. Include the following in your email (80 words): A description of the policy Reference to an attachment of...
-
Wollongong Group Ltd, of New South Wales, Australia, acquired its factory building about 10 years ago. For several years the company has rented out a small annex attached to the rear of the building....
-
Oligopolistic models are based on behavioral assumptions. One behavioral assumption associated with differentiated product markets is that price increases will not be matched, but price decreases...
-
Determine the following indefinite integrals. Check your work by differentiation. 1/2y dy
-
Fraud deterrence is centered on the fear of getting caught and the fear of getting punished. In your opinion, which is stronger and why?
-
a. In each of the following independent problems, design an unbiased random sampling plan, using an electronic spreadsheet or a random number generator program. The plan should include defining the...
-
In the arrangement shown in the figure below, an object of mass m = 4.00 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.00 m. (Ignore the...
-
A cascade system is composed of two ideal refrigeration cycles, as shown in Fig. 9.28. The high temperature cycle uses R-410a. Saturated liquid leaves the condenser at 40C, and saturated vapor leaves...
-
Approximately when did modern humans migrate to Australia? O 100,000 yBP 40,000 yBP 15,000 yBP 5,000 yBP
-
Why is the information in the notes to the financial statements important to financial statement readers? Choose the best answer. Select answer from the options below It is helpful for determining...
-
How might globalization be a problem for a successful national company that is intent on going international? What advantages would the national company have by going international? Provide an...
-
Do you think there should be some international standard for labor rights? If so, what should that standard be and how should it be enforced?
-
Today, Green Branch Coffee's employees began the process of forming a union. The Director of Human Resources wants you to discuss a few important facts about unions so that the coffee shop managers...
-
State and overall position regarding the meaning and function of leadership in organizations today.
-
Using a four-month moving average on the data given in the spreadsheet, determine one-step-ahead and two-step-ahead forecasts for July through December 2016. Compare their performance. (Hint: In the...
-
Ashlee, Hiroki, Kate, and Albee LLC each own a 25 percent interest in Tally Industries LLC, which generates annual gross receipts of over $10 million. Ashlee, Hiroki, and Kate manage the business,...
-
1. The final score in a soccer game is 6 to 4. How many different halftime scores are possible? 2. Each day, Gloria dresses in a blouse, a skirt, and shoes. She wants to wear a different combination...
-
Find the probability that at least two people in a group of size n = 5 select the same card when drawing from a 52-card deck with replacement. Determine the group size n for which the probability of...
-
1. In an Olympic swimming event, two of the seven contestants are American. The contestants are randomly assigned to lanes 1 through 7. What is the probability that the Americans are assigned to the...
-
Long Weekend Ltd suffered a severe drop in sales and profit performance for the year ended 30 June 2019. The income statement revealed that net sales were $1 500 000 with a profit of $310 000. Unit...
-
TMP Human Resource Consulting had the following contribution margin income statement for the year ended 2019. Required Answer each of the following independent situations. (a) Explain how an...
-
Selcombe, Selcombe and Selcombe Media are three generations of the one family involved for nearly 50 years in providing public relations services. The firm is preparing its fees budget for the year...
Study smarter with the SolutionInn App