Given the following simplex tableau, determine if the solution represented is optimal.If it is optimal, state the solution.If it is not optimal, determine the next pivot element.POHONx1 x2 x3 s1 s2 z0 -7 012X N92211 -20 12013 0 0729210 151 135symbolic formatting help

Introduction: The Simplex method uses slack variables, tableaus, and pivot variables to solve linear…

Answered: Given the following simplex tableau,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Formulate but do not solve the problem.The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $44 and $28 per acre, respectively. Jacob Johnson has $17,200 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? (Let x and y denote the number of acres of corn and wheat, respectively.)   = 500   = 17,200
Formulate a system of equations for the situation below and solve.A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table. Sleeveless Short-Sleeve Long-Sleeve Cutting 9 12 15 Sewing 22 24 28 Packaging 6 8 8 The cutting, sewing, and packaging departments have available a maximum of 87, 176, and 52 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? sleeveless      ___ dozen short-sleeve      ___ dozen long-sleeve      ___dozen
Formulate a system of equations for the situation below and solve.A manufacturer of women's blouses makes three types of blouses: sleeveless, short-sleeve, and long-sleeve. The time (in minutes) required by each department to produce a dozen blouses of each type is shown in the following table. Sleeveless Short-Sleeve Long-Sleeve Cutting 9 12 15 Sewing 22 24 28 Packaging 6 8 8 The cutting, sewing, and packaging departments have available a maximum of 87, 176, and 52 labor-hours, respectively, per day. How many dozens of each type of blouse can be produced each day if the plant is operated at full capacity? sleeveless      ___ dozen short-sleeve      ___dozen long-sleeve      ___ dozen
The problem below involves three variables. Solve it with the simplex method, Excel, or some other technology.A medical clinic performs three types of medical tests that use the same machines. Tests A, B, and C take 15 minutes, 30 minutes, and 1 hour, respectively, with respective profits of $120, $260, and $530. The clinic has four machines and four workers available. One person is qualified to do test A, two to do test B, and one to do test C. If the clinic has a rush of customers for these tests, how many of each type should it schedule in a 8-hour day to maximize its profit? ? A tests ? B tests ? C tests
Q2. Complete the following iteration tableau of Maximization problem of LPP and comment on the nature of the optimal solution. Basic variables XI Cbi X2 $2 Solution 51 $3 2 -1 30 XI X2 20 $2 gzi 1. 1,
A pet food wholesaler produces a dog food mixture that is sold to pet retail outlets in bags of 10 pounds each. The food mixture contains turkey and beef. The cost per pound of each of these ingredients is as follows: Ingredient Cost/poundTurkey $2.00Beef $5.50 Each bag must contain at least 5 pounds of turkey. Moreover, the ratio of turkey to beef must be at least 2 to 1. The optimal mixture of the ingredients is: Turkey: __________ pounds (Round your answer to the nearest pound) Beef: ___________ pounds (Round your answer to the nearest pound) The total value of the optimal solution is $________ per bag of dog food. (Round your answer to the nearest dollar)
The Rainwater Brewery produces beer. The annual fixed cost is $150,000, and the variable cost per barrel is $15. Price is related to demand, according to the following linear equation: v=75000-1200p. The objective function is Z= [ Select ] + [Select ] + [Select ] The optimal solution = [ Select]
Write your solutions on a separate paper and attach it to this sheet. You are welcome to share ideas with others in the class, but be sure the work you submit is your own. Part I For the following linear program, solve using the simplex method. In the table, trace the sequence of corner points in the simplex procedure. Beginning with the solution in your initial tableau, record the basic solution, and the value for z. You may not use all of the rows in the table. Corner Point (x, y) Value of z Part II Maximize z = 17x + 20y, subject to -7x+10y≤ 50 3x + 5y < 90 4x + 5y ≤ 105 x≤ 20, x ≥ 0, y ≥ 0 Increase in z Write your final tableau, and verify it represents the optimal solution. Values of Slack Variables (S1, S2, S3) Now, solve the same problem, but use column 1 as the first pivot column, instead of column 2. Record your sequence of pivots in the table below, as you did in Part I. Corner Point (x, y) Value of z Increase in z Slack Variables (S1, S2, S3) Notice that this nonstandard…

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Given the following simplex tableau, determine if the solution represented is optimal. If it is optimal, state the solution. If it is not optimal, determine the next pivot element. x1 0 1 2 9 2 x2 x3 s1 s2 z -7 0 1 -20 12 2 1 0 0 15 13 0 0 1 2 9 2 1 135