Solve each of the following linear programs using the simplex algorithm You shouldgive the initial tableau and each further tableau produced during the execution of thealgorithm. If the program has an optimal solution, give this solution and state its objectivevalue. If it does not have an optimal solution, say why.Ideally you should indicate the highlighted row and columns in each pivot step as wellas the row operations you carry out.2.maximize 2x₁ +4₂3subject to-2x1 + x3 ≤ 3,1x₁2x2 + 4x3 ≤ 2,x1 + x23x3 ≤ 2,2x1x₂ + x3 ≥ −6,I1, I2, I3 20

Linear programming (LP) is a mathematical optimization technique used to find the best solution to a…

Answered: Solve each of the following linear…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 45P

See similar textbooks

Similar questions

You want to take out a 450,000 loan on a 20-year mortgage with end-of-month payments. The annual rate of interest is 3%. Twenty years from now, you will need to make a 50,000 ending balloon payment. Because you expect your income to increase, you want to structure the loan so at the beginning of each year, your monthly payments increase by 2%. a. Determine the amount of each years monthly payment. You should use a lookup table to look up each years monthly payment and to look up the year based on the month (e.g., month 13 is year 2, etc.). b. Suppose payment each month is to be the same, and there is no balloon payment. Show that the monthly payment you can calculate from your spreadsheet matches the value given by the Excel PMT function PMT(0.03/12,240, 450000,0,0).
The method for rating teams in Example 7.8 is based on actual and predicted point spreads. This method can be biased if some teams run up the score in a few games. An alternative possibility is to base the ratings only on wins and losses. For each game, you observe whether the home team wins. Then from the proposed ratings, you predict whether the home team will win. (You predict the home team will win if the home team advantage plus the home teams rating is greater than the visitor teams rating.) You want the ratings such that the number of predictions that match the actual outcomes is maximized. Try modeling this. Do you run into difficulties? (Remember that Solver doesnt like IF functions.) EXAMPLE 7.8 RATING NFL TEAMS9 We obtained the results of the 256 regular-season NFL games from the 2015 season (the 2016 season was still ongoing as we wrote this) and entered the data into a spreadsheet, shown at the bottom of Figure 7.38. See the file NFL Ratings Finished.xlsx. (Some of these results are hidden in Figure 7.38 to conserve space.) The teams are indexed 1 to 32, as shown at the top of the sheet. For example, team 1 is Arizona, team 2 is Atlanta, and so on. The first game entered (row 6) is team 19 New England versus team 25 Pittsburgh, played at New England. New England won the game by a score of 28 to 21, and the point spread (home team score minus visitor team score) is calculated in column J. A positive point spread in column J means that the home team won; a negative point spread indicates that the visiting team won. The goal is to determine a set of ratings for the 32 NFL teams that most accurately predicts the actual outcomes of the games played.
STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 3
In linear programming problems, you always need to include a(n) ___________ constraint, to ensure that all decision variables are greater than or equal to 0. Group of answer choices positive time production non-negativity
Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O O
Use the Huntington-Hill numbers listed in the table to assign seats as indicated. (REVIEW UNIT 5 - CHAPTER 4) Eleven seats on a hospital board are to be apportioned between doctors, nurses, and administrators. Use the given table of Huntington-Hill numbers to list the order in which the seats on the board will be apportioned. Begin by apportioning one seat to each group. Current Representation 1 (D)octors (N)urses (A)dministrators 7,200 2,812 11,250 3,750 1,875 1,125 750 937 2,400 468 281 1,200 720 3 4 5. 187 480 O D. N, A, A, N, A, D, N, A, N, A O D. N. A, A. N, D. A, N, D. A, N O D, N, A, N, A, A, D, N, A, A, N O D, N, A, A, D, A, N, N, A, N, D
Recall the production model: Max Max s.t. s.t. 10x Suppose the firm in this example considers a second product that has a unit profit of $5 and requires 2 hours of labor time for each unit produced. Use y as the number of units of second product produced. (a) Show the mathematical model when both products are considered simultaneously. 5x ≤ 40 x ≥ 0 x ≥ 0, y ≥ 0
Chikana Company produces and sells rattan baskets. The number of drifts produced are the corresponding total production costs for six months, which are representatives for the year, are as follows: Month Units Produced Production Costs P 4,000 8,000 6,000 7,500 8,500 7,250 April Мay 500 700 June 900 July August September 600 800 550 Required: Solve for the variable and fixed cost component using: a.) High- Low Method b.) Least- Squares Regression
TRUE OR FALSE In the simplex minimization method, optimality is signaled by the presence of all positive values in the Cj-Zj row
Consider the linear program max 4y_{1} + 5y_{2} s.t. - y_{1} + y_{2} <= 4 y_{1} - y_{2} <= 10 y_{1}, y_{2} >= 0 (a) Show graphically that the model is unbounded.
Consider the ordered bases B = space V of upper triangular 2 × 2 matrices. a. Find the transition matrix from C to B. TB = 2 1 -2] and C = for the vector 2 -2 b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is [M]c = 22 B [M]B= c. Find M. M =
WHAT WLL HAPPEN IF THERE IS A CHANGE IS ONE OF THE OBJECTIVE FUNCTION COEFFICIENT? A. SLOPE OF THE OBJECTIVE FUNCTION LINE ALWAYS WILL CHANGE B. OPTIMAL SOLUTION ALWAYS WILL CHANGE C. ONE OR MORE OF THE DECISION VARIABLES ALWAYS WILL CHANGE D. ALL OF THE ABOVE E. NONE OF THE ABOVE

SEE MORE QUESTIONS

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS